Anuj Kaul
email: anujkaul@soe.ucsc.edu

Katia Obraczka

Mateus A S Santos
email: msantos@dca.fee.unicamp.br

Christian E Rothenberg

Thierry Turletti
email: thierry.turletti@inria.fr

Dynamically Distributed Network Control for Message Dissemination in ITS

We propose D2-ITS, a flexible and extensible framework to dynamically distribute network control to enable message dissemination in Intelligent Transport Systems (ITS). By decoupling the control-from the data plane, D2-ITS leverages network programmability to address ITS scalability, delay intolerance and decentralization. It uses a distributed control plane based on a hierarchy of controllers that can dynamically adjust to environment-and network conditions in order to satisfy ITS application requirements. We demonstrate the benefits of D2-ITS through a proof-of-concept prototype using the ns-3 simulation platform. Results indicate lower message delivery latency with minimal additional overhead.

I. INTRODUCTION

Vehicular communication is expected to support Intelligent Transport Systems (ITS) 1 , in which vehicles exchange information to self-drive, coordinate traffic flow, communicate road conditions, avoid accidents, etc. Vehicle-to-vehicle and vehicle-to-infrastructure communication is thus a basic building block to enable and support ITS.

Message dissemination services such as Road Hazard Warning (RHW) [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF], [START_REF]Intelligent transport systems; vehicular communications; basic set of applications; specification of cooperative awareness basic service[END_REF] are notable examples of emerging ITS applications. RHW services aim at alerting road users of relevant events, including traffic jams and hazardous conditions employing vehicular communication and cooperation in real time. ITS services and applications pose significant challenges due to their stringent low latency, reliability, scalability, and geographic decentralization requirements.

In order to address ITS' challenges and enable efficient wireless connectivity on wheels, ITS deployments rely on infrastructure-based wireless communication such as IEEE 802.11 variations or LTE. However, while 802.11p [START_REF] Jiang | IEEE 802.11p: Towards an international standard for wireless access in vehicular environments[END_REF], a standard ITS solution, suffers from scalability issues [START_REF] Amadeo | Enhancing IEEE 802.11 p/WAVE to provide infotainment applications in VANETs[END_REF], the main concern for LTE-based communication is latency due to its centralized architecture. As surveyed in [START_REF] Araniti | LTE for vehicular networking: a survey[END_REF], such limitations motivate heterogeneous wireless communication technologies as promising ITS solutions.

Leveraging the emergence of the Software-Defined Networking (SDN) paradigm, Software-Defined Vehicular Ad hoc NETwork (SD-VANET) architectures have been proposed [START_REF] Truong | Software defined networking-based vehicular adhoc network with fog computing[END_REF], [START_REF] Ku | Towards software-defined VANET: Architecture and services[END_REF]. SD-VANETs rely on the separation between network control and data planes, resulting in increased network programmability that enables vehicles to react and adjust to 1 http://www.etsi.org/technologies-clusters/technologies/intelligent-transport dynamically changing environmental-and networking conditions.

As discussed in more detail in Section VI, SD-VANETs have demonstrated the benefits of using SDN's decoupling of network control from data when compared to "traditional" VANET architectures (e.g., employing multi-hop ad hoc network routing [START_REF] Ku | Towards software-defined VANET: Architecture and services[END_REF]). However, current architectures either: [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF] rely on logically centralized control plane, or (2) use a static control distribution approach, bothe of which are not compatible with ITS' scalability, geographic decentralization, and latency requirements. Additionally, heterogeneous wireless communication technologies in which vehicles are equipped with multiple wireless interfaces for improved connectivity and reliability have not yet been explored.

In this paper, we introduce D2-ITS, a flexible and extensible framework that can dynamically distribute network control to address the scalability, delay intolerance, and decentralization requirements of ITS applications. To the best of our knowledge, D2-ITS is the first framework to employ a distributed control plane which: [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF] isdecoupled from the data plane, and (2) is based on a control hierarchy that can dynamically adjust to current environment and network conditions in order to support ITS application requirements. As such, the contributions of this paper include: (1) D2-ITS' distributed network control plane architecture and design; (2) D2-ITS implementation in support of ITS' Road Hazard Warning (RHW) message dissemination; and (3) Proof-of-concept D2-ITS prototype demonstrating that our framework provides lower message delivery latency with minimal additional overhead.

The remainder of the paper is organized as follows. Section II introduces the D2-ITS architecture. ITS RHW message dissemination application is presented in Section III. In Section IV we describe D2-ITS' design and implementation and in Section V we evaluate our D2-ITS prototype to support RHW services. We review related work in Section VI and present final remarks and directions for future work in Section VII.

II. D2-ITS ARCHITECTURE

Our approach to addressing the requirements of Intelligent Transport Systems (ITS) leverages the basic principle underlining the Software-Defined Networking (SDN) paradigm, i.e., the decoupling of the control-and the data planes. From ITS' perspective, the main benefits resulting from control-data plane separation include increased agility to detect and react to the underlying system/network dynamics which provides better support for ITS' stringent quality-of-service requirements.

On the other hand, SDN's logically centralized control plane is not compatible with ITS' scalability and latency requirements, as well as its geographic-and administrative decentralization. For example, control plane scalability limitations have been discussed along with approaches to partially solve them in [START_REF] Karakus | A survey: Control plane scalability issues and approaches in software-defined networking (SDN)[END_REF].

In D2-ITS, we leverage network programmability enabled by the separation between the network control-and data planes to achieve flexibility and agility. However, we go a step further by proposing a logically distributed network control plane which can dynamically adjust to current environment conditions and network characteristics to support ITS' scalability, delay intolerance, and decentralization. D2-ITS' distributed control plane employs a hierarchy of "controllers" as exemplified in Figure 1. In this example ITS scenario, vehicles connect to road-side units (RSUs) which in turn are connected through a back haul network (e.g., Radio Base Stations, or RBSs). Controllers are placed at RSUs and control vehicles within their "domain". As illustrated in Figure 2, an RSU's domain is defined by its communication range. We consider that RSUs employ low range communication technologies such as IEEE 802.11 and its variants. At the next level up the control hierarchy, controllers are placed at RBSs and control their own domain, which could span RSUs within the RBS' communication range. Control is thus decentralized since controllers do not necessarily have complete state information about the network and participants.

Control Plane

As illustrated in Figure 1, control plane communication happens through the "east-west" interface between controllers at the same hierarchical level ("horizontal" east-west communication) or between controllers at different levels ("vertical" east-west communication). Controllers use the equivalent to SDN's southbound interface API to communicate with nodes (i.e., vehicles) they control, which are equipped with software switches, e.g., SDN-enabled (not shown in the figure). RSUs are also equipped with software switches such that they can relay data messages.

Data Plane

Data is forwarded according to routing/forwarding policies established by the domain's controller, the local RSU in our example scenario. We should point out that since RSUs and RBSs are also part of the data forwarding infrastructure, they can also participate in data forwarding. For instance, if node 1 in Domain A (see Figure 1) needs to communicate with node 2 in Domain B, it will do so through Domain A's RSU which will relay traffic to Domain B's RSU. Alternatively, as indicated in Figure 1, data can flow directly between two domains as long as the controllers establish a direct data path.

Figure 2 illustrates how control domains can be defined for infrastructure-based ITS scenarios, i.e., ITS deployments using infrastructure-based wireless communication (e.g., through 2, controllers located at RSUs or RBSs will control nodes within their communication range. If a node is located within range of more than one RSU, the node can decide which RSU will function as its controller using criteria such as the RSUs' RSSI, etc. As previously pointed out, the RSUresident controller can configure vehicles in its domain to send data packets directly to it using a vehicle-to-infrastructure (V2I) model, so that communication goes through a lowlatency backbone. Vehicle-to-vehicle (V2V) communication could also be employed for data forwarding. Additionally, as shown in Figure 2, mobile infrastructure (e.g., mobile gateways in vehicles) capable of V2V communication can be used to extend coverage of stationary infrastructure.

III. ROAD HAZARD WARNING (RHW) APPLICATION

D2-ITS' current design is motivated by ITS message dissemination applications, such as Road Hazard Warning (RHW) services [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF], [START_REF]Intelligent transport systems; vehicular communications; basic set of applications; specification of cooperative awareness basic service[END_REF] which use V2I communication to disseminate messages amongst vehicles.

Road Hazard Warning (RHW) [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF], [START_REF]Intelligent transport systems; vehicular communications; basic set of applications; specification of cooperative awareness basic service[END_REF] is an event-based road message dissemination service specified by the European Telecommunications Standards Institute (ETSI). It defines a variety of events including traffic jams, hazardous conditions and messages that will be generated to alert road users (e.g., cars, trucks) of such events 2 .

For example, Decentralized Environmental Notification Messages (DENMs) [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF] are mainly used to provide the necessary alerts in the case of emergency situations (e.g., eminent risk of collision) or warnings, e.g., in the event of a road congestion. As such, DENMs should be conveyed through the ITS infrastructure and delivered to road users in the geographic area affected by the event, or "relevance area" [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF].

Cooperative Awareness Messages (CAMs) [START_REF]Intelligent transport systems; vehicular communications; basic set of applications; specification of cooperative awareness basic service[END_REF], on the other hand, carry signaling information. CAM's contents vary according to the type of RHW service. They may carry information about vehicle location, vehicle type, as well as time of day, vehicle speed, etc. Section IV-C describes how we implement RHW message dissemination atop our D2-ITS framework.

A. Infrastructure-Based Communication

We consider scenarios in which RSUs are deployed along roads and highways to provide network coverage using shortor medium-range technologies. In our D2-ITS framework, the RSU is a natural host for the controller, which manages its "domain" using specialized control applications running atop the controller. For instance, control applications can be tailored to cope with specific features of the area being serviced. For example, some regions can be sparser while others can be more dense.

Infrastructure-based communication in support of RHW services can employ only stationary infrastructure, i.e. RSUs. Alternatively, since in some cases deploying RSUs can be either technically or financially not viable, mobile, device-todevice communication capable gateways can be used to extend the scope of RSUs. They can connect vehicles that would be disconnected otherwise. Figure 3 illustrates the case in which a source node transmits messages that are forwarded both by the fixed infrastructure as well as mobile gateways in order to reach all their destinations. Mobile gateways can also be used to interconnect RSUs in regions where they are sparsely deployed.

B. RHW Message Dissemination

Below, we highlight some of the main RHW's message dissemination assumptions, features, and requirements.

• Vehicle-to-infrastructure communication: V2I communication is the default method of message dissemination; alternatively, the controller can establish direct vehicleto-vehicle (V2V) paths. As previously discussed, the controller can also designate a vehicle as a gateway node, which would then relay messages to nodes for which it serves as gateway. Note that in the latter two cases, vehicles would need to be capable of V2V communication.

• Vehicle-to-vehicle communication: V2V communication can also be used to disseminate messages; it will be based on match-action tables installed by the appropriate controller.

• Vehicle position: a vehicle knows its position (e.g., using GPS) and transmits it periodically using CAMs to a controller in its communication range. • Relevance area based message delivery: application messages should be routed to the appropriate relevance area; note that vehicles may be moving in and out of relevance areas. • Relevance area: the relevance area of a given message is computed by the corresponding controller. • RSU coverage: RSUs have limited coverage so vehicles could be outside the range of an RSU. As previously pointed out, RSUs can extend their coverage by designating a vehicle in its range to act as a gateway to forward messages to other vehicles outside the RSU's range. Note that there may be cases in which vehicles are not covered by an RSU. • Message delivery priority: RHW messages require different delivery priorities. For instance, messages that convey emergency situations will have higher priority over messages carrying information about general road conditions.

IV. D2-ITS DESIGN AND IMPLEMENTATION

Using Road Hazard Warning services (RHW) as our use case allows us to show D2-ITS' ability to handle RHW's message delivery requirements. As the basis for our implementation, we use the Libfluid [START_REF] Vidal | The libfluid openflow driver implementation[END_REF] open-source controller and the Open vSwitch (OVS) software switch [START_REF] Pfaff | The design and implementation of open vSwitch[END_REF]. As we describe in detail in this section, some of our contributions include the design and implementation of the east-west interface for controller-to-controller communication, as well as the extension of the southbound controller-to-vehicle to include the new message types required by RHW services.

A. Message Types and Dissemination

The types of messages supported in our current D2-ITS implementation follow ETSI's ITS specifications [START_REF] Etsi | Intelligent transport systems; vehicular communications; basic set of applications; specifications of decentralized environmental notification basic service[END_REF], [START_REF]Intelligent transport systems; vehicular communications; basic set of applications; specification of cooperative awareness basic service[END_REF] for RHW services as described in Section III.

• Decentralized Environmental Notification Messages (DENMs) are forwarded by D2-ITS' data plane and can be of the following types:

-Emergency are time-sensitive data plane messages sent by vehicles to their connected controller to convey information about nearby accidents, eminent risks, etc. They have the highest delivery priority. Controllers flood emergency messages to vehicles in their domain. We opted to follow the ETSI "awareness range" criteria, i.e., emergency messages are delivered to vehicles in the neighborhood using a time-to-live approach. We should point out that the D2-ITS framework can be adjusted to account for different message delivery criteria; -Warning are also data plane messages. They are sent by vehicles to their connected controller to report abnormal situations on the road such as road congestion or traffic jams. Warnings are disseminated by controllers to vehicles within their relevance area. Depending upon the type of warning and the extension of the area it affects, the controller can also forward such message to peer controllers, which in turn will decide how to forward the message further.

• Cooperative Awareness Messages (CAMs) are control plane messages which are sent periodically from a vehicle to a controller. They typically carry information about vehicles such as their current location, speed, etc. Controllers use location updates to compute relevance areas, compute and install routes in vehicles. This is similar to the concept of Local Dynamic Map (LDM) defined by ETSI [START_REF] Etsi | Intelligent Transport Systems (ITS); Vehicular Communications; Basic Set of Applications; Local Dynamic Map (LDM)[END_REF]. These messages are also exchanged between controllers to exchange information about their respective domains.

• User Addition Requests: are another type of control plane messages. They are sent by a vehicle to the controller to which the vehicle trying to connect. This message also serves to authenticate the vehicle with the controller. If security is not enforced, user addition requests are used for node identification purposes only.

• Controller HELLO are control plane messages used to advertise controller presence and build peering relations between pairs of controllers.

CAM and DENM messages are implemented using Open-Flow 1.3's experimenter message. Experimenter messages are Fig. 4. D2-ITS controller's processing of CAM messages used in OpenFlow 1.3 as a way to enable extensions to the protocol without the need of a protocol version update. In our implementation, we use the payload of an experimenter message to carry the RHW messages described above (e.g., CAMs and DENMs). As shown in Figure 6, which illustrates the format of the experimenter message, we use the header to specify the message type and the length of its payload. The message type differentiates between different types of CAM and DENM messages.

B. D2-ITS Controller

As we elaborate in Section IV-A, each vehicle connected to a controller can send CAM and DENM messages. CAM messages are also exchanged between neighboring controllers to notify each other about their respective domain. The flowcharts shown in Figure 4 and Figure 5 summarize how the D2-ITS controller handles the different types of messages it receives.

Upon reception of a CAM message from a vehicle, the controller updates the corresponding information about the vehicle in its local database. Similarly, the controller updates its local database with the domain information of the neighboring controller upon the reception of CAM messages.

When DENM warning message is received by the controller it gets routed to the relevance area through backhaul network using east-west interface. Message routing is decided using the domain information of the neighboring controllers in the local database updated via CAM messages. Thus, geographic routing of the warning messages depends on the area relevant to the corresponding event.

DENM emergency message needs immediate action and hence is broadcasted by the controller upon its reception. The broadcasting of emergency messages is localized to the domain of the controller.

C. D2-ITS Prototype

We used the ns-3 simulator3 in conjunction with its Direct Code Execution (DCE) 4 module to prototype our framework. Using DCE allows execution of live code atop the ns-3 stack that enabled us to use open-source controllers, standardized APIs and software switches that are widely used. As previously pointed out, D2-ITS enabled vehicles are based on the Open vSwitch (OVS) [START_REF] Pfaff | The design and implementation of open vSwitch[END_REF] software switch with OpenFlow suppport [START_REF] Mckeown | Openflow: enabling innovation in campus networks[END_REF]. Libfluid [START_REF] Vidal | The libfluid openflow driver implementation[END_REF] was used to provide a lightweight controller implementation. One main new feature we added to the Libfluid controller is the east-west interface, which enables controller-to-controller communication and OpenFlow experimenter messages. Additionally, as described in Section IV-A, we implemented D2-ITS control-(e.g., CAMs) and data plane messages (i.e., DENMs) using OpenFlow experimenter messages. To this end, we added new experimenter message types as well as the logic to generate and parse them.

Figure 7 illustrates D2-ITS' prototype modules and their interactions. As shown in the figure, our customized versions of OVS and libfluid run atop the ns-3 userspace through DCE, enabling the OpenFlow protocol for any node interface. Node interfaces such as LTE and 802.11 variants can work atop a Linux kernel stack or atop a simulated ns-3 stack. Note that the RSU is implemented based on the modified libfluid controller while a vehicle is based on the modified OVS switch. Additionally, D2-ITS supports the use of mobile controllers, a feature that we discuss in Section V-C.

V. D2-ITS EVALUATION

As proof of concept, we showcase how our D2-ITS framework supports ITS applications. Our experiments aim at demonstrating the benefits of using a decentralized control plane approach for Road Hazard Warning services.

A. Experimental Methodology

We ran our experiments using the D2-ITS prototype built on ns-3/DCE. We conducted a side-by-side comparison between • D-ITS: two stationary RSUs (node 2 and node 3), each co-located with a controller, are interconnected through a wireless network. Vehicles in an RSU's range connect to the controller hosted by the RSU over IEEE 802.11 ad hoc mode; RSUs communicate through a point-to-point backhaul network; • C-ITS: devices are associated to a single network-wide controller using the cellular network. In particular, as shown in Figure 9, we use an LTE network where the LTE base station, eNodeB, (node 0) is connected to the centralized controller through a backhaul network. Message generation: In our experiments, vehicles send periodic RHW messages that are either warning or emergency messages and are conveyed over V2I communication. As described earlier, warning messages should be routed to a relevance area (which may include multiple domains), while emergency messages should be broadcast locally in the domain. Warning messages are generated every 3 seconds and emergency messages every 7 seconds. Vehicle mobility: A grid of size 1000x800 meters was created to represent the road. In order to provide a realistic road network scenario, we simulate platoon of vehicles traveling on the road with a certain speed while the source node, which is also moving, sends warning and emergency messages. A few stationary cars are also placed along the roadside. We use SUMO (Simulation of Urban MObility) [START_REF] Krajzewicz | Recent development and applications of SUMO -Simulation of Urban MObility[END_REF] to generate realistic vehicle mobility traces which were used as input to our ns-3/DCE simulations.

Table I presents the main parameters used for the D-ITS and C-ITS scenarios. In the case of C-ITS, the backhaul network uses ns-3's point-to-point abstraction to connect the eNodeB LTE base station and the controller. We set the backhaul network delay to 100 milliseconds which is the upper bound delay expected for LTE mobile backhaul [START_REF] Piri | Performance of lte uplink for iot backhaul[END_REF]. For a fair comparison, we use the same parameters for the D-ITS backhaul network, which connects the RSUs. Note that the It is worth pointing out that in D-ITS, forwarding decisions are distributed across different controllers, while in C-ITS, a single controller is in charge of forwarding decisions. Another difference is that the C-ITS scenario imposes the maintenance of a network-wide database. In D-ITS, on the other hand, controllers do not need to keep a global view of the network state. Evaluation metrics: Motivated by ITS' low delay requirements, we measure end-to-end latency as the time it takes for data messages (both warning and emergency) to be delivered from the source node to nodes in the message's relevance area. We report latency results for both emergency and information messages. We also compute overhead as the ratio between the number of data bytes over the total number of control bytes generated.

B. Results

We present results for mobile and stationary destination nodes in the relevance area. Each data point in the latency graphs below are averaged over 10 runs. Latency variations between different runs were negligible, therefore we do not show them. In the D-ITS scenario, nodes 7 to 13 are moving towards the relevance area, while nodes 5 and 6 are stationary located in the relevance area. In C-ITS, nodes 5 to 11 are mobile, while nodes 3 and 4 are stationary.

Figures 10 and11 show how message delivery latency varies with time in the D-ITS scenario for a stationary-and mobile destination, respectively. Figure 12 shows latency results for a mobile node in the C-ITS scenario. We should point out that in the C-ITS scenario, there is no difference in delivery latency for stationary-or mobile nodes (so we only show a single latency graph for the C-ITS scenario). This is because nodes are always connected to the centralized controller. We should also note that the graphs shown for an individual node are representative (i.e., show similar results and trends) of that node's category (e.g., all mobile-or all stationary nodes in the experiment). Note that the stationary vehicles, namely nodes 5 and 6 in the D-ITS scenario, remain connected to RSU node 3 throughout the lifetime of the experiment, while mobile vehicles (nodes 7-13) connect to RSU node 3 only during the time they are in RSU node 3's range. In the C-ITS scenario, vehicles are always connected to the centralized controller (node 0). Consequently, as shown in Figure 12, we observe that: (1) delivery latency is constant throughout the experiment (except for some outliers that will be discussed below); (2) there is no difference in latency for emergency or warning messages.

In contrast, in the D-ITS scenario, emergency messages are delivered only to the vehicles located in the area affected by the event that triggered the message and are consistently delivered with much lower latency when compared to the C-ITS scenario. In our experiments, the average latency for emergency messages is 18ms (accounting for the outliers shown in the graphs) while in the C-ITS case, it is 142ms, which is the same for warning messages, as previously pointed out. Note that in Figure 11 messages were not delivered when the vehicle was outside the relevance area.

In the case of warning messages, overall, they experience lower latency in the D-ITS scenario (average latency of 110ms) when compared to C-ITS (average latency of 142ms). Warning message latency depends on the location of the sender relative to the receiver. For instance, in Figure 10, up to about 116 seconds, the source node is connected to RSU node 2, forcing warning messages to travel across different domains through decentralized controllers so they can reach the relevance area covered by RSU node 3. This results in latency varying from 115 to 120 milliseconds.

We calculated the overhead for both scenarios and our results show that the overhead incurred by the D-ITS scenario is only 6.5% higher than C-ITS's overhead.

Figure 10 also shows that the source node cannot connect to a controller between 110 to 145 milliseconds. The reason is that 802.11 communication range is not enough to provide connectivity in the region between RSU nodes 2 and 3 (recall that RSUs are 740m away from each other). During this period, the source node does not send any messages until it connects to RSU node 3 at second 145. Such connection allows messages to be disseminated within a single domain with latency results varying from 7 to 10 milliseconds.

Figure 11 depicts latency results for warning messages received by a mobile vehicle (node 7). As previously noted, even though we show results for node 7, they are similar to every other mobile node in the experiment (i.e., nodes 7-13). According to the figure, node 7 only receives warning messages while in the relevance area and connected to RSU node 3. This explains the zero latency points in the figure, which represent messages not being received by the node. We observe that, in some cases, emergency and warning messages experienced considerably higher latency when compared to the average latency. Vehicle mobility increases the chance of such anomaly in the simulated experiment. Also, latency can increase as vehicles reach the edge of the RSU coverage area. In summary, our experiments highlight that the proposed framework can yield lower message delivery latency for Intelligent Transport Systems services such as RHW. In particular, we show that emergency messages can be delivered with significantly lower latencies (in our experiments, one order of magnitude lower) when compared to a centralized control plane approach with only a slight increase in overhead.

C. Discussion

As described previously, D2-ITS' current implementation focused on ITS' RHW services. However, D2-ITS can be extended to include other features and functionality so that it can be used by other ITS applications. Below we describe some of these extensions. Vehicle-to-vehicle communication: as mentioned in Section III-A, our framework can be extended to support V2V communication. We provided the example of a mobile gateway that extends the domain of a RSU by forwarding data packets to neighbors (Figure 3). One of the challenges is to provide the controller with sufficient information to control a gateway. For instance, the controller should be aware of nodes in the gateways' vicinity, including their position. Such information would enable the controller to define message relevance areas, i.e., decide which nodes should receive which data messages.

Vehicle-controller discovery: our framework allows vehicles to establish a connection with a controller for exchanging control and data packets. Even though we did not explore how such connection can be established dynamically, it is an important challenge to be addressed. OpenFlow allows multiple controller connection for a single switch with the restriction of defining a single controller in charge (or a master controller). However, there is no protocol for dynamic switch-controller association. In our experiments, it is possible to predict when a vehicle will be in the range of an RSU, and thus, of a controller. This helps in defining when a vehicle should become part of a controller's domain.

Mobile controller: disconnections between vehicles and controllers may happen very often in ITS due to mobility, RSU coverage, etc. One way to mitigate control plane disconnections is to use mobile controllers. For example, in Figure 3, a gateway could act as a controller through a delegation process [START_REF] Santos | Decentralizing SDN's control plane[END_REF], i.e., a higher layer controller could offload tasks to the new instantiated controller. The work in [START_REF] Hassas Yeganeh | Kandoo: a framework for efficient and scalable offloading of control applications[END_REF] provides an example of task offloading using local controllers, but does not address challenges such as dynamically defining what tasks should be delegated and when they should be offloaded.

VI. RELATED WORK

VANETs: some of the main challenges of VANETs relate to efficient and reliable message dissemination. Many protocols usually mitigate the broadcast storm problem using techniques for broadcast suppression (e.g., [START_REF] Wisitpongphan | Broadcast storm mitigation techniques in vehicular ad hoc networks[END_REF]), limiting the number of relay nodes. A common method to nominate relay nodes in VANETs is based on node position and moving direction (e.g., [START_REF] Sun | GPS-based message broadcasting for inter-vehicle communication[END_REF], [START_REF] Mariyasagayam | Enhanced multihop vehicular broadcast (MHVB) for active safety applications[END_REF]). The appropriate selection of relay nodes also impacts in reliability. For instance, mobility prediction can be employed for improved message delivery rate [START_REF] Lai | A reliable broadcast routing scheme based on mobility prediction for VANET[END_REF].Reliabilty is also a challenge for VANETS in ITS due to the link stability. The work in [START_REF] Taleb | A Stable Routing Protocol to Support ITS Services in VANET Networks[END_REF] proposes the grouping of vehicles according to their velocity. The results have shown increase in link duration, reduction in the number of link-breakage events and increase in the end-to-end throughput.

Software Defined VANETs: Ku et al. [START_REF] Ku | Towards software-defined VANET: Architecture and services[END_REF] propose an architecture for software-defined VANETs. The architecture assumes a logically centralized intelligence for the entire VANET system. Based on simulation results which evaluate routing performance, the authors show that SDNs are beneficial for VANETs when compared to wireless, multihop ad-hoc network (MANET) solutions. They demonstrate that transmission power adjustment is another feature that can be provided using SDN.

Petit et al. [START_REF] Petit | Protocols for roadside-toroadside data relaying over vehicular networks[END_REF] investigate the feasibility of vehicles acting as data relays between RSUs. They consider the scenario in which RSUs have no wired or wireless connectivity between them and use vehicle mobility to relay data amongst RSUs. They find that the throughput obtained is directly proportional to the peak rate of the wireless channel used for vehicle-toroadside communication.

DeVANET [START_REF] Kazmi | DeVANET: decentralized software-defined VANET architecture[END_REF] proposes a decentralized software-defined VANET architecture in which each "domain" has its own centralized SDN controller. A "root" controller receives domain information such as link state and host presence from domain controllers. From its description in [START_REF] Kazmi | DeVANET: decentralized software-defined VANET architecture[END_REF], DeVANET does not consider dynamic control distribution in response to application needs and current network and environment conditions. Additionally, its implementation and consequently experimental evaluation are quite limited.

Other efforts such as [START_REF] Luo | sdnMAC: a software defined networking based mac protocol in VANETs[END_REF] and [START_REF] Liu | A software defined network architecture for geobroadcast in VANETs[END_REF] consider SDN-enabled RSUs for VANETs. This approach allows dynamic path computation by an SDN controller. An interesting concept is the RSU cloud [START_REF] Salahuddin | Software-defined networking for rsu clouds in support of the internet of vehicles[END_REF] in which a customized RSU can host services for vehicles. It employs SDN to dynamically instantiate, replicate, and/or migrate services.

Software Defined Networking: the concept of local controllers was firstly advocated by Kandoo [START_REF] Hassas Yeganeh | Kandoo: a framework for efficient and scalable offloading of control applications[END_REF] in order to reduce the load on the global controller. Local controllers filter the number of new flow requests. The work in [START_REF] Schmid | Exploiting locality in distributed SDN control[END_REF] investigates the relation between algorithms to manage distributed controllers and algorithms to maintain local controllers. Usman et al. [START_REF] Usman | A softwaredefined device-to-device communication architecture for public safety applications in 5G networks[END_REF] propose a hierarchical D2D communication architecture for public safety applications that also uses the concept of local controllers. Formation and management of mobile clouds of devices are the main goal of the architecture.

The framework proposed here provides a flexible control plane that can automatically adjust as a function of the dynamics of the underlying environment in order to address application requirements. Control can be distributed as needed: for example, controllers can be instantiated at different ITS control levels, e.g., at RSUs or in vehicles within groups of vehicles. That way, decisions can be made locally using only locally-relevant information, for example in order to satisfy stringent latency requirements. Local control also allows the system to scale as well as improve its robustness to connectivity disruptions. The use case scenario presented in the previous section shows a proof-of-concept of our D2-ITS prototype and demonstrates that it can achieve lower message delivery latency with minimal additional overhead.

VII. CONCLUSION AND FUTURE WORK

In this paper, we propose the D2-ITS framework which uses network programmability to support message dissemination services for Intelligent Transport Systems. We describe D2-ITS decentralized control plane architecture, design, and prototype implementation. Our proof-of-concept experiments using the ns-3/DCE simulation platform show that D2-ITS yields lower message delivery latency with minimal additional overhead.

We plan to pursue the following directions of future work: control plane load balancing and fault tolerance, security, and administrative decentralization and autonomy. We also plan to carry on further experiments using Mininet-Wifi [START_REF] Fontes | Mininet-WiFi: Emulating software-defined wireless networks[END_REF].

Fig. 1 .

 1 Fig. 1. Example D2-ITS scenario

Fig. 3 .

 3 Fig. 3. RHW communication using gateways

Fig. 5 .

 5 Fig. 5. D2-ITS controller's processing of DENM messages

Fig. 7 .

 7 Fig. 7. D2-ITS prototype

Fig. 8 .

 8 Fig. 8. D-ITS scenario

Fig. 10 .

 10 Fig. 10. Distributed scenario (D-ITS). Latency graph for a stationary vehicle (vehicle 5) in the relevance area.

Fig. 11 .

 11 Fig. 11. Distributed scenario (D-ITS). Latency graph for a mobile vehicle (vehicle 7) approaching the relevance area.

Fig. 12 .

 12 Fig. 12. Centralized scenario (C-ITS). Latency graph for a mobile vehicle (vehicle 3) in the relevance area.

Figure 10

 10 Figure 10 also shows that emergency messages are localized to a single domain, resulting in delivery with low latency. A stationary vehicle does not receive emergency messages until time 145 seconds, i.e., when source node finds itself in the same domain as its (stationary) destination.

TABLE I SIMULATION

 I PARAMETERS.

	Parameter	D-ITS	C-ITS
	Simulation time	300 s	300 s
	Number of nodes	14	12
	Node speed	10.15 m/s	10.15 m/s
	Event report interval (Information)	3 s	3 s
	Event report interval (Emergency)	7 s	7 s
	Communication	802.11 ad hoc	LTE
	Bandwidth	11 Mbps	25 Mbps
	Distance between RSUs	740m	-
	Estimated RSU range	145m	-
	Backhaul delay	100ms	100ms
	Backhaul data rate	2 Mbps	2 Mbps
	Grid size	1000x800m	1000x800m

More information on ETSI Intelligent Transport Systems standards is available at http://www.etsi.org/technologies-clusters/technologies/intelligenttransport.

https://www.nsnam.org/

https://www.nsnam.org/overview/projects/direct-code-execution/

VIII. ACKNOWLEDGMENTS This work has been partially supported by NSF under grant CNS 1321151 and by the French Government (National Research Agency, ANR) through the Investments for the Future Program under grant ANR-11-LABX-0031-01. Mateus A. S. Santos is currently with Ericsson Research.


Sophie Dartois
email: sophie.dartois@upmc.fr

Sophanarith Mom
email: sophanarith.mom@gmail.com

Hélène Dumontet
email: helene.dumontet@upmc.fr

Abdelwahed Ben Hamida

Abdelwahed Ben Hamida
email: abdelwahed.ben_hamida@upmc.fr.

An iterative micromechanical modeling to estimate the thermal and mechanical properties of polydisperse composites with platy particles: application to anisotropic hemp and lime concretes

Keywords: Hemp and Lime Concretes, Multiscale Modeling, Anisotropy, Platy Particles, Porosity, Finite Element Analysis, Microstructure, Homogenization, Polydisperse Composites

and research institutions in France or abroad, or from public or private research centers.

An iterative micromechanical modeling to estimate the thermal and mechanical properties of polydisperse composites with platy particles: Application to anisotropic hemp and lime concretes

Introduction

Over the past thirty years building materials reinforced with vegetal products, and more specifically vegetal concretes, have made a remarkable headway in the construction field due to their slight environmental impact. Hemp and lime concretes, also known as hempcretes, are one of the most commonly used bio-based construction material for walls since their outbreak in the late 1980s [START_REF] Woolley | Low Impact Building[END_REF], [START_REF] Ingrao | Energy and environmental assessment of industrial hemp for building applications: A review[END_REF]. Not only are they made of sustainable resources usually considered as by-products of the fiber and oil industries, but their production has a very low carbon footprint. They have also proved to be particularly efficient as far as thermal insulation is concerned allowing thus some substantial energy savings [START_REF] Boutin | Etudes des caractéristiques environnementales du chanvre[END_REF], [START_REF] Ip | Life cycle greenhouse gas emissions of hemp-lime wall constructions in the uk[END_REF], [START_REF] Ingrao | Energy and environmental assessment of industrial hemp for building applications: A review[END_REF], [START_REF] Collet | Thermal conductivity of hemp concretes: variation with formulation, density and water content[END_REF]. On the other hand, their mechanical performances stay rather modest which explains why they are currently only used as filling materials for walls, roofs and floors, together with wooden load-bearing structures. Vegetable concrete manufacturers in association with project managers aim at improving the mechanical resistance of vegetable concretes while preserving the insulation properties of the latter. They also need the establishment of building norms that will enable a wide use of this new type of materials. Comprehensive constitutive models can provide valuable help to make this step easier. They allow indeed to perform collections of numerical simulations (so called "digital experiments") with varying parameters, such as the physical nature, shape or spatial arrangement of the constituents. In the framework of a large optimization and certification campaign, the purpose of this work is to predict the thermal and mechanical properties of hemp and lime concretes at the end of their manufacturing process by means of a numerical multi-scale modeling technique. Such technique allows to pay a special attention to the quite complex microstructures of this class of materials.

Hemp-lime concretes (HLC) are obtained by mixing hemp hurds commonly referred to as hemp shives with a lime based binder. The latter is an air-slaked lime produced in presence of pozzolans, and water. The mixture obtained is then processed and casted (which often includes a compaction stage) and is eventually dried. The very nature of the material and its manufacturing process make several modeling issues arise. First of all the specific morphology and spatial distribution of hemp shives have to be taken into account. Hemp shives are indeed elongated platy particles cut in the wooden core of the plant stem. They have a rectangular parallelepipedic shape with a moderate slenderness Fig. 1(b). Hemp shives exhibit an orthotropic behavior as they are bored through by micro tubular ducts originally forming the sap distribution network. The spatial arrangement of shives together with their own behavior is at the origin of the material global anisotropy. The compaction phase of the manufacturing process tends moreover to align shives in several parallel planes or strata, in-creasing thus a potential initial anisotropy [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF], [START_REF] Tronet | Study of lime hemp concrete (lhc) -mix design, casting process and mechanical behaviour[END_REF], [START_REF] Williams | A method for the assessment of the internal structure of bio-aggregate concretes[END_REF]. The architecture of the material also depends on the concrete formulation, i.e. on the quantities of shives and lime introduced. Some hemp and lime concretes may appear as an entanglement of hemp particles maintained together thanks to local lime bridges when the shives rate is high, whereas others have a more classical microstructure, i.e. hemp particles embedded in a lime matrix phase Fig. 1(a). A related issue to deal with is the high porosity rate as it may represent up to 70% of the concretes volume [START_REF] Arnaud | Experimental study of parameters influencing mechanical properties of hemp concretes[END_REF], [START_REF] Evrard | Transient hygrothermal behaviour of hemp-lime materials[END_REF], and sometimes nearly 80% [START_REF] Glé | Acoustical properties of materials made of vegetable particles with several scales of porosity[END_REF], [START_REF] Collet | Comparison of the hygric behaviour of three hemp concretes[END_REF].

Pores and voids are indeed present at both meso and microscales. Mesopores (i.e. whose size is close to the size of hemp shives) can be the result of the very architecture of the material when the lime rate is low. They appear as well in the matrix phase when the lime rate is high and the forming process lacks mixing. As noted earlier tubular microvoids can also be observed in shives. The porosity of hemp shives is indeed commonly considered as a little higher than 80% [START_REF] Lanos | Formulation and Implementation[END_REF], [START_REF] Picandet | Characterization of Plant-Based Aggregates[END_REF]. Some micropores may as well appear in the lime matrix as the result of chemical reactions during the drying phase. The presence of these two categories of voids (mesopores and micropores) and their potential closure during the compaction phase of the manufacturing process has to be taken into account in the constitutive modeling of the hemp concretes in use [START_REF] Diquelou | Influence of binder characteristics on the setting and hardening of hemp lightweight concrete[END_REF]. Scale transition modeling techniques including morphology features appear thus as an appropriate tool to account for all these complex morphological effects when trying to estimate the properties of hempcretes.

Micromechanical models have been developed over the past sixty years to determine the global behavior of heterogeneous materials depending on their local microstructures. A series of models can be found in the literature using analytical homogenization schemes, often based on the fundamental Eshelby's ellipsoidal inclusion model [START_REF] Eshelby | The determination of the elastic field of an ellipsoïdal inclusion and related problems[END_REF]. Very few are nevertheless dedicated to materials reinforced with rectangular parallelepipedic particles more or less randomly distributed in the material, for which analytical solutions are missing [START_REF] Banks-Sills | On the effect of particle shape and orientation on elastic properties of metal matrix composites[END_REF], [START_REF] Lacoste | On the validity of the self-consistent scale transition model for inclusions with various morphologies[END_REF], [START_REF] Lacoste | A multi-scale analysis of materials reinforced by inclusions randomly oriented in the ply plane[END_REF]. As computational resources increase numerical full-field finite element simulations on detailed Representative Volume Elements (RVE) could appear as a convenient solution to this problem. The RVE could either be numerically designed or digitally reconstructed from experimental imagery like computed tomography. In both cases, the generation of the RVE reveals itself quite complex when dealing with contacts between the particles and the size of the RVE as evidenced by several articles on fibrous media and especially wood-based ones [START_REF] Lux | 3d characterisation of wood based fibrous materials: an application[END_REF], [START_REF] Walther | Microstructural analysis of lignocellulosic fiber networks[END_REF], [START_REF] Malmberg | Measurement of fibre-fibre contact in three-dimensional images of fibrous materials obtained from x-ray synchrotron microtomography[END_REF], [START_REF] Viguié | Finding fibres and their contacts within 3d images of disordered fibrous media[END_REF], [START_REF] Dirrenberger | Towards gigantic rve sizes for 3d stochastic fibrous networks[END_REF] among others. As a consequence the filling rates of the materials numerically designed from scratch are generally below those of the category of concretes considered here. In the case of computed tomography, computer resources needed are high for both the reconstruction phase and the subsequent finite element solving procedure. But the most limitating fact in the use of this type of approach is that the meshing step entails some remodeling of the real microstructure in order to avoid distorted elements and mesh size problems. Some microstructural artefacts are therefore artificially added to RVE potentially with an effect on the identification of the global properties of the material.

As the materials at stake in this paper do not have a precisely controlled microstructure given their forming process it is here chosen, as several authors did previously [START_REF] Arnaud | Innovations in design with emphasis on seismic, wind, and environmental loading: quality control and innovations in materials/hot-weather concreting[END_REF], [START_REF] Collet | Thermal conductivity of hemp concretes: variation with formulation, density and water content[END_REF], [START_REF] Akkaoui | Experimental and micromechanical analysis of the elastic properties of wood-aggregate concrete[END_REF], to focus on much more time efficient modeling methods.

More precisely this paper deals with an iterative multiscale modeling which has been developed to describe the behavior of highly-filled materials with polydispersed heterogeneities. The approach at stake is inspired by the differential scheme defined by McLaughlin [START_REF] Mclaughlin | A study of the differential scheme for composite materials[END_REF], enhanced by Norris [START_REF] Norris | A differential scheme for the effective moduli of composites[END_REF] and proposed for linear porous media by Zimmerman [START_REF] Zimmerman | Elastic moduli of a solid containing spherical inclusions[END_REF]. The modeling pro-cedure follows the manufacturing process of granular composites materials in which heterogeneities are gradually introduced in a matrix phase whose properties evolve through the process. The creation of a given medium is thus achieved through the sequential production of intermediate partiallyfilled media. The effective constitutive laws (as defined by [START_REF] Rocha | On the effective conductivity of dilute dispersions: general theory for inclusions of arbitrary shape[END_REF], [START_REF] Hashin | The elastic moduli of heterogeneous materials[END_REF], [START_REF] Aboudi | Mechanics of composite materials: a unified micromechanical approach[END_REF]), of the corresponding intermediate composite can be obtained thanks to any homogenization technique since the volume fraction of heterogeneities is very small for a given step. This method was first proposed for non linear and porous media such as clayes [START_REF] Brini | Aging damage of immersed syntactic foams under coupled effects of pressure and aqueous corrosion[END_REF] and dealt with composites with identical particles. It was next extended to non-linear media such as porous media [START_REF] Benhamida | Clay compaction modelling by homogenization theory[END_REF], [START_REF] Smaoui | Micro-macro approaches coupled to an iterative process for nonlinear porous media[END_REF] or periodic damaged cemented soils [START_REF] Bouchelaghem | Nonlinear mechanical behaviour of cemented soils[END_REF]. In the meantime the approach was extended to study polydisperse composites such as syntactic foams [START_REF] Zouari | A micromechanical iterative approach for the behaviour of polydispersed composites[END_REF]. It is nevertheless to be noted that the papers listed above dealt either with materials with spherical inclusions, allowing thus an analytical solution of the local problem, or with periodic materials.

The modeling purpose of the present work is therefore to widen the scope of the iterative multiscale modeling to materials with platy particles of various geometrical dimensions, orientations and physical properties with a special attention paid to the resulting anisotropy of the effective macroscopic behavior of the composites. To this aim the model is coupled with dedicated finite element simulations and analytical procedures allowing to take into account the orientation of the particles in the material. The main features of these procedures are presented in Section 2. Simulations are then carried out in Section 3 with the aim of estimating the thermal and mechanical linear effective properties of hemp and lime concretes. The results stemming from these simulations are eventually confronted to experimental data from the literature. More precisely the iterative multiscale modeling is first put into practice to identify the properties of the constituents of hempcretes for various compaction degrees. The results obtained are then used as input data to estimate the thermal and mechanical properties of a collection of moderately compacted concretes on the one hand, and of a specific concrete being subjected to increasing compaction degrees during its manufacturing phase on the other hand.

Model description and implementation

General framework of the iterative multiscale modeling

The iterative multiscale modeling follows the manufacturing process of granular composites materials and is schematically represented on Fig. 2. As stated in the previous section it is inspired by the differential scheme [START_REF] Mclaughlin | A study of the differential scheme for composite materials[END_REF]. At each step j a composite material is created by adding a small fraction δf (j) of inclusions (pores or particles) in a consistent matrix phase. A structural analysis, commonly referred to as "local problem", is then performed on the corresponding Representative Volume Element (RVE) in order to determine its effective thermal and mechanical behavior.

Thanks to a homogenization procedure the properties of an equivalent homogeneous medium are identified and the latter is finally used as the matrix phase for the following step. This process is repeated n times until the targeted filling rate f = n j=1 δf (j) is reached, and the filling rate at step j is:

f (j) = δf (j) (1 -f ) + j p=1 δf (p) (1)
Composite Materials Homogeneous Equivalent Media

Step 1

δf (1) Homogenization First Intermediary Homogeneous Equivalent Medium

Step 2 δf (2) Homogenization ] [

Step n δf (n)

Homogenization

Homogeneous Equivalent Medium with the targeted filling rate In a thermal linear framework, at each step j of the iterative procedure, the Representative Volume Element (RVE) noted Ω is submitted to a macroscopic thermal gradient G. This induces a microscopic heat flux q(x) which depends on the position x ∈ Ω and whose variations in each phase are described thanks to the Fourier law of heat conduction:

q(x) = -K α (x) grad T (x), x in Ω α , α ∈ {m, inc} (2)
with α equal to m standing for matrix, or to inc for inclusion. Ω α is the volume of the phase α in the RVE

Ä Ω = Ω m ∪ Ω inc ä . T (x)
is the temperature at point x in Ω, and K α is the second order tensor of thermal conductivity in phase α.

The equivalent second order conductivity tensor K * (j) to determine at each homogenization step j links the macroscopic temperature gradient G to the macroscopic flux Q (j) thanks to Eq (3):

Q (j) = ¨q(j) (x) ∂ = -K * (j) . ¨grad T (j) (x) ∂ = -K * (j) .G (3)
where . denotes classical volume average.

K * (j) explicitly depends on the properties of the phases of the local problem, i.e. K α , α ∈ {m, inc}. The iterative principle implies that for a given step j, the conductivity tensor of the matrix phase K m corresponds to the homogenized conductivity tensor identified at the end of the previous step K * (j-1) , namely K m = K * (j-1) . As a consequence, the equivalent behavior searched at step j has the following form inspired by the classical solution by Eshelby [START_REF] Eshelby | The determination of the elastic field of an ellipsoïdal inclusion and related problems[END_REF]:

K * (j) = K * (j-1) +f (j) Ä K inc -K * (j-1) ä : ¨a(j) Ä x, f (j) , K inc , K * (j-1) ä ∂ Ω i (4
) where K inc is the conductivity tensor of the inclusion added (with K inc = K air if the inclusion added at step j is a pore), and a (j) represents the localization tensor at step j.

In a linear elastic context the same representative volume element Ω is considered. A distinction is nevertheless here made between pores with no rigidity Ω p , elastic inclusions Ω inc , and the matrix

Ω m Ω = Ω p ∪ Ω inc ∪ Ω m .
The RVE is submitted to a macroscopic strain E which causes microscopic stress and strain fields, respectively σ(x) and ε(x), to appear in the RVE. They are locally linked via the rigidity tensor of each phase: C α (x), with once again α equal to m for matrix, or inc for inclusion.

σ(x) = C α (x) : ε(u), x ∈ Ω α , α ∈ {m, inc} (5)
The equivalent fourth order rigidity tensor C * (j) to determine at the end of each homogenization step j links the macroscopic stress tensor Σ (j) , which is the classical volume average of the microscropic stress field σ (j) (x), to the macroscopic strain field applied on the RVE thanks to the relationship Eq (6):

Σ (j) = ¨σ(j) (x) ∂ = C * (j) : E = C * (j) : ¨¨ε(u (j) ) ∂∂ (6)
where ε(u) is the average of local strains ε(x) in a RVE containing pores. In a similar way as the thermal context, the homogenized tensor C * (j) explicitly depends on the rigidity tensor at step j -1 since C m = C * (j-1) . If the inclusion added to the matrix at step j is an elastic particle with a rigidity tensor C inc , the equivalent behavior at this step has the following form:

C * (j) = C * (j-1) + ϕ (j) Ä C inc -C * (j-1) ä : ¨A(j) Ä x, f (j) , C inc , C * (j-1) ä ∂ Ω inc (7)
where ϕ (j) is the volume fraction of elastic particles in the composite at step j and A (j) represents the strain localization tensor. Note that if φ (j) is the volume fraction of pores in the composites at step j then f (j) = ϕ (j) + φ (j) . If a pore is added to the matrix phase at step j, the equivalent behavior is given by:

C * (j) = C * (j-1) -φ (j) C * (j-1) : ¨¨A (j) Ä x, f (j) , C * (j-1) ä ∂∂ Ω p (8)
In this iterative homogenization procedure, the volume fraction of heterogeneities in each local problem to solve is very small. As a consequence the properties of the successive homogeneous media defined in Eqs ( 3) or ( 6) can be identified regardless of the homogenization technique used to this aim. More precisely, all the classical Eshelby based homogenization methods, even the original dilute scheme [START_REF] Eshelby | The determination of the elastic field of an ellipsoïdal inclusion and related problems[END_REF], can be put into practice at each step with similar results on the effective properties of the final composite as evidenced in the literature [START_REF] Benhamida | Clay compaction modelling by homogenization theory[END_REF]. It is yet to be noted that the filling rate at the end of the whole procedure can reach any level, including the highest ones (i.e. superior to 80%).

The iterative structure of the multiscale modeling considered makes it moreover particularly convenient and efficient when it comes to estimate the behavior of highly-filled materials with multiphysic and complex microstructures. The fraction of heterogeneity introduced at each step can indeed vary in shape, size, nature and orientation from one step to another. An illustration of this major asset can be found in [START_REF] Zouari | A micromechanical iterative approach for the behaviour of polydispersed composites[END_REF] where the iterative multiscale modeling was used to estimate the behavior of syntactic foams which are highly contrasted and polydispersed composites. Another example is the work on cemented soils (pores and sand) [START_REF] Vu | A micromechanical numerical modelling approach for the homogenization of grouted sands[END_REF], in which the nature of the inclusion varied from one homogenization step to another. The results thus obtained were in good concordance with experimental results in both studies; but it is to be noted that the investigations were limited to isotropic materials with spherical inclusions. In order to estimate the thermal and mechanical characteristics of materials with elongated platy shaped particles such as hemp-lime concrete or any other morphological features, finite element simulations and other extra subroutines are developed and coupled to the iterative scheme. They are detailed in the following section starting with the description of the real geometry of the particles.

Coupling with Finite Element Analysis to account for the shape of particles

The iterative multiscale scheme described in subsection 2.1 does not depend on the solving procedure used for the local structure problem at each step j. For materials with spherical or ellipsoidal inclusions analytical models are particularly efficient, but when heterogeneities are polyhedral, the use of numerical solving methods is necessary. This is the case of materials filled with rectangular parallelepipedic particles on which this study is focused. A first step to improve the iterative multiscale method is consequently to combine it with Finite Element Analysis (FEA) simulations when solving each intermediate local problem. In practice, at each step j a local problem is solved on a RVE by doing the following:

1. The RVE is composed of a single oriented parallelepipedic particle, embedded in a matrix phase.

2. Since the modeling scheme does not depend in its principle on the geometry nor on the slenderness of the particle, and since the estimation of the properties of hemp concretes is eventually at stake in this study the shape factor of the particle introduced at each step is close to the one of hemp shives Fig. 3(a). For more precisions on hemp shives granulometry one can refer to [START_REF] Benfratello | Thermal and structural properties of a hemplime biocomposite[END_REF], [START_REF] Williams | A method for the assessment of the internal structure of bio-aggregate concretes[END_REF], [START_REF] Glé | Acoustical properties of materials made of vegetable particles with several scales of porosity[END_REF], [START_REF] De Bruijn | Moisture fixation and thermal properties of lime-hemp concrete[END_REF], [START_REF] Schwarzova | Thermal stress effect on density changes of hemp hurds composites[END_REF].

3. The spatial orientation of the particle is characterized by the three angles θ, ψ and ϕ defined on Fig. 3(b).

4. The properties of the matrix phase are updated at each step (i.e. chosen equal to the homogenized behavior obtained at step j -1).

5. The global size of the RVE is accommodated in order that the volume fraction of particles in the material is f (j) at the end of the step.

At the end of the process one obtains the equivalent homogeneous orthotropic behavior of a media filled with a targeted proportion f of particles all oriented in the same direction. This media will be referred to as a single-oriented material throughout the paper.

In order to avoid the creation of a collection of meshes each corresponding to a possible orientation of the particle, a reference mesh, partially represented on Fig. 3(c), is used together with rotation matrices P(θ, ψ, ϕ). Those matrices allow indeed to deduce the effective properties of a material containing a particle in an arbitrary direction (θ, ψ, ϕ) from those of a material with a single particle whose axes are aligned with the ones of the RVE i.e. (θ = 90°, ψ = 0°, ϕ = 0°). In the thermal framework, the effective conductivity tensor of a material with a particle in an arbitrary direction can thus be obtained by using the following relationship: K * (θ, ψ, ϕ) = P T K * (90°, 0°, 0°) P.

The same process can be used in an elastic context to obtain the effective rigidity tensor C * (θ, ψ, ϕ) = P T (P T C * (90°, 0°, 0°) P) P. The implementation of this digital process was validated thanks numerical simulations run on a virtual orthotropic test material in which all the particles have the exact same geometry and are aligned in the same direction θ = 90°, ψ = 0°, ϕ = 0°. The results of these simulations were compared with salient results from simulations run on periodic microstructures in both thermal an elastic frameworks. For low filling rates both methods provide the same results in terms of effective conductivities and elastic properties. For higher filling rates the periodic approach is yet limited because of mesh distorsion when particles get too close.

Orientation of the particles and potential induced anisotropy

The case of more complex microstructures is logically debated in this subsection. More precisely, the composites considered here are made of a matrix phase containing a large number of particles oriented in m distinct directions. They will be referred to as poly-oriented materials as opposed to single-oriented materials defined in Section 2.2. Families of particles are also defined, each family corresponding to one of the m orientations classically defined by the three angles (θ, ψ, ϕ) represented on Fig. 3(b).

A scenario for the introduction of the particles is here proposed. It is inspired in its principle by the methodology used when dealing with the granulometric polydispersion of hollow spheres in syntactic foams [START_REF] Zouari | A micromechanical iterative approach for the behaviour of polydispersed composites[END_REF]. In the present study the orientation of the particles is the discriminating parameter rather than the size of the particles, leading to some adjustments. From this point, for an easier description of how the iterative method can be used to model poly-oriented materials it is chosen to present its practical application on materials containing particles evenly distributed on the m spatial directions, meaning that all the families contain the same number of particles. It is yet to be noted that this is absolutely not a restriction of the model. In the specific case of particles evenly distributed on m directions the iterative modeling is composed of n series of m successive homogenization substeps each one performed with a particle belonging to a different family as illustrated on Fig. 4. If f is the overall volume fraction of particles in the composite, then the proportion of family i is f i = f /m, and the volume fraction of particles introduced during an homogenization substep is therefore δf i = f i /n = f /(n × m). At the end of each series of homogenization the symmetries of the final intermediate equivalent homogeneous material depend on the number and orientation of the families as well as on the intrinsic behavior of the particles.

In the special case of fully isotropic materials the number of families m tends to infinity and the effective behavior of the final intermediate equivalent homogeneous material at the end of a series k is expected to be isotropic. As a consequence it can be obtained thanks to a single simulation on a RVE with a particle oriented in the direction (90°, 0°, 0°) followed by, first the use of the rotation matrix as described in Section 2.2, and then an integration phase on the three angles covering all the spatial directions instead of a succession of m homogenization steps. In the thermal context for instance the effective conductivity K * of the intermediate homogeneous medium at the end of a series k can thus be obtained in practice thanks to the following explicit integral : Step 2 M 1i M 1m

K * = 1 2π 2 2π 0 Ç 2π 0 Å π 0 sin θ P T (θ, ψ, ϕ) K * (90°, 0°, 0°) P(θ, ψ, ϕ) dθ ã dϕ å dψ = 1 3 (K * 11 (90°, 0°, 0°) + K * 22 (90°, 0°, 0°) + K * 33 (90°, 0°, 0°) ) Id (9)
Intermediary Homogeneous Equivalent Medium (end of Serie 1) where Id stands for the identity matrix.

Serie 2 M 21 M 22 Step j M 2i M 2m Serie n-1 M n-1 1 M n-1 2 M n-1 i M n-1 m Serie n M n 1 M n 2 M n i M n m Targeted Homogeneous Equivalent Material
In It is worth mentioning that another scenario could have been envisioned for the introduction of the particles by inverting the nesting order of the loops on the families and on the increments of the iterative modeling itself. This alternate scenario has been tested on fully isotropic materials during Mom's Ph.D. and the results obtained have been compared to those given by classical analytical solutions for materials filled with spherical inclusions. For a contrast higher to ten between particles and matrix in terms of thermal conductivity and Young modulus the alternate scenario leads to incorrect results in terms of effective properties, with a relative error superior to 10% when compared to results obtained thanks to the scenario represented on Fig. 4 and the analytical solving.

On Fig. 5 are reported the results obtained for a contrast on Young modulus close to 350 (mechanical properties listed in Table 1). The mechanical properties of a particle of hemp wood (hemp shiv) have been identified from the properties of loose shives thanks to an inverse method in which loose shives are considered as a two phased material (hemp particles + air) whose effective properties are known. The iterative micromechanical modeling was used to identify which values of Young modulus and Poisson coefficient for hemp particles lead to the experimentally identified macroscopic isotropic properties of loose shives. The results obtained were similar to those calculated by Cerezo in her Ph.D. work thanks to a self-consistent scheme. Fig. 5 shows, as expected, that in the case of isotropic media the volume fraction of particles has an impact on the effective global behavior but not the shape nor dimension of the particles. The relative error between results from numerical simulations run on materials with elongated particle randomly distributed and analytical solutions remains indeed inferior to 2% for the whole range of filling rate. A sensitivity study has also been carried out regarding the size of the increment δf i representing the volume fraction of heterogeneities included in the matrix phase at each step. This study showed that for an increment δf i = 1% the relative error between the results stemming from both scenari is less than 3% within the range of contrast between the phases usually encountered in hemp and lime concretes. δf = 1% is therefore the value chosen for all the simulations presented in this paper.

Phase Young Modulus (MPa) Poisson ratio

For composites with a limited number of material symmetries, a combination of the methods described in the previous paragraphs can be used. For instance an estimation of the global behavior of a transverse isotropic composite can be obtained thanks to Eq.( 9) with θ = 90°and without integrating over θ when the isotropy is in plane (e 1 , e 2 ). The behavior within the isotropy plane corresponds then to the one of a composite reinforced by circular inclusions, but the estimation of the behavior off axis requires a 3D numerical solving.

When materials are purely anisotropic due to a discrete spatial orientation of particles, a homogenization step is carried out on a RVE containing a single particle, then the effective thermal and mechanical behaviors of intermediate media each corresponding to a family of particles are obtained thanks to rotation matrices. Then the effective global linear behavior of the composite is eventually estimated via a weighted summation on the various intermediate K * and C * whose weights correspond to the volume fraction of the particles in each direction.

Influence of the nature and behavior of the phases on effective properties.

The discreet process on which the iterative multiscale modeling is based proves itself very convenient when it comes to study composites containing inclusions of different natures such as pores and elastic particles. The mechanical or thermal properties of the inclusion can indeed be modified at each homogenization step just like its orientation was in the previous section. The question of the introduction sequence of the various inclusions is then raised. One can either choose to alternate the introduction of the inclusions or to introduce all the particles of a given type in a row. In a linear framework and for the category of materials eventually at stake, i.e. hemp concretes, simulations results indicate that the introduction sequence has a very limited impact on the effective anisotropic properties (and especially when the contrast is reduced as it is the case in the thermal case). This is why this point is not investigated here. In Sections 3.2 and 3.3 an alternate introduction of phases (hemp shives and pores) is carried out for all simulations. Issues concerning the orientation and nature of particles are consequently addressed the same way.

The numerical solving of the local problems developed in Section 2.2 allows as well to take into account the presence of interphases between particles and matrix in an explicit manner. Accounting for the interphase only requires to create an actual layer of elements around the particle in the digital RVE on which each local problem is solved. The introduction of interphases within the iterative multiscale modeling has been briefly investigated in the form of a feasibility study. Simulations have been successfully performed on virtual study materials constituted of an isotropic matrix filled with particles wrapped in an interphase with a few number of elements through its constant thickness; the latter being set to ensure that the volume of the interphase is equal to the volume of the particle. This configuration has been chosen on the basis of micrographies of plant-based concretes [START_REF] Nozahic | Design of green concrete made of plant derived aggregates and pumice-lime binder[END_REF], [START_REF] Diquelou | Influence of binder characteristics on the setting and hardening of hemp lightweight concrete[END_REF]. In vegetal concretes the porosity of particles makes it indeed possible for some water sorption to happen during the manufacturing phase of the concretes. This water may later be evacuated leading to the formation of a halo of modified matrix around the particles. The presence of this interphase tends to lower the global mechanical properties of concretes and should be accounted for when trying to estimate the global rigidity of hemp concretes, but one of the current impediment to the continuation of the numerical modeling work undertaken on the subject is the lack of experimental identification for the mechanical and thermal properties of the interphases. Meanwhile solutions are sought after in order to prevent this phenomenon from happening, for instance by waterproofing particles before mixing thanks to wax coats [START_REF] Al-Mohamadawi | Influence of lignocellulosic aggregate coating with paraffin wax on flax shive and cement-shive composite properties[END_REF], or by chemical treatments [START_REF] Stevulova | Water absorption behavior of hemp hurds composites[END_REF]. The numerical multiscale modeling developed here makes it possible as well to take into account the intrinsic anisotropic behavior of the particles. In order to validate this point simulations have been carried out to estimate the effective behavior of a single-oriented composite (i.e. composed of a matrix phase containing platy particles and all oriented in the same direction). In a first test case particles are isotropic whereas in a second test case particles are transverse isotropic, with the orthotropy axes matching the geometrical symmetry axes of the particles. The corresponding thermal properties are listed in Table 2.

Phase Conductivity (W.m -1 .K Results obtained are shown on Fig. 2.4. As expected, the anisotropy is increased when the particles are transverse isotropic. When the filling rate is equal to one, the effective behavior of the oriented composite obviously matches the behavior of the particles. This is of course due to the fact that the orthotropy axes match the loading axes in that case. These results prove if needed the necessity to consider the anisotropy of particles as a major input data when modeling oriented materials, and show the ability of the digital procedure to account for it.

(W.m 1 .K 1 ) K ⇤ 11 K ⇤ 22 K ⇤ 33 K ⇤ 11 K ⇤ 22 K ⇤ 33

Estimate of thermal and elastic properties of hemp concretes.

A wide range of hemp concretes mixes exist depending on their final use (floors, walls, roofs, coating,...). They mainly differ in terms of filling and compaction rates (i.e. density and manufacturing process). Simulations, have been performed in both thermal and elastic contexts, in order to estimate the effective properties of a collection of hemp concretes thanks to the iterative multiscale model whatever the compaction rates of the different concretes are. Composites studied here are on the one hand concretes in which the spatial distribution and orientation of the particles is even in each direction and on the other hand concretes with a high compaction rate such as breeze blocks or laboratory samples.

Preliminary identification of the behavior of the constituents

One of the most popular lime matrix used for the manufacture of hemp concretes is Tradical PF70 whose thermal conductivity and mechanical properties are close to those reported in Table 1 & 2. Lime matrix is here considered as a microporous material. In order to take into account the evolution of the properties of the lime matrix with respect to its porosity rate, simulations have been carried out with the numerical iterative multiscale model on RVEs composed of a spherical pore embedded in a lime matrix phase. The isotropic thermal and mechanical properties obtained for airslaked lime are displayed on Fig. 7(a) and Fig. 7(b) (right ordinate axis).

The identification of the behavior of shives is more complicated since it is quite difficult to perform experiments on a single hemp shiv given its size. Several authors have chosen to identify the properties of the wooden particles from data collected on loose shives samples by using an inverse analysis. A first estimate can indeed be obtained by considering loose shives as a heterogeneous two-phase material made of shives embedded in an air matrix and by using various homogenization schemes. The thermal and mechanical properties of a hemp particle can for instance be determined thanks to a self-consistent scheme based on a RVE with spherical inclusions randomly distributed in space as it was done in Cerezo's Ph.D. work partially reported in [START_REF] Arnaud | Innovations in design with emphasis on seismic, wind, and environmental loading: quality control and innovations in materials/hot-weather concreting[END_REF]. The iterative numerical multiscale modeling can also be used under the same assumptions and with the same input data. This leads to similar results as the ones obtained by Cerezo (reported in Tables 1 and2) when considering the particle isotropic: E part. = 1.5M P a and ν part. = 0.1, k part. = 0.110 W.m -1 .K -1 . This identification can nevertheless be enhanced by taking into account the heterogeneity and anisotropy of hemp shives. Hemp shives can schematically be seen as a bundle of connected micro-ducts made of vegetal matter and filled with air [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF], [START_REF] Collet | Comparison of the hygric behaviour of three hemp concretes[END_REF], [START_REF] Schwarzowá | Investigation of observed changes in treated hemp hurds[END_REF]. The properties of the vegetable matter constituting the walls of the ducts can be estimated by performing an inverse analysis on a two-phase isotropic medium (air and vegetal matter). The volume fractions of both phases in a non compacted state are identified of thanks to measures on density found in the literature [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF] (volume fractions: f air 78% and f vege. matter 22%). As ducts are parallel, the longitudinal behavior of the hemp particle (ducts direction) is obtained via a classical weighted average on the behavior of the constituents (example for thermal conductivity: k longi. particle = f vege. matter . k vege. matter + f air . k air ). The 2D version of the iterative multiscale modeling is eventually used to determine the transverse behavior. With this method, the complete effective transverse isotropic behavior of a hemp particle is obtained ranging from its free state to a highly compacted state (i.e. no porosities), as shown on Fig. 7(a) and Fig. 7(b) (left ordinate axis) together with results obtained for the lime matrix.

The evolution of the thermal and elastic properties of hemp shives and lime with respect to porosity is clearly non-linear. As expected the spindle shaped curves depicting the behavior of transverse isotropic hemp shives frame the results found in the literature when considering the particles isotropic. The latter where obtained via an inverse identification from experimental results on loose shives using a self-consistent scheme on a material with spherical particles. As far as the isotropic lime matrix is concerned the results obtained almost interpolate the isolated results obtained by the same authors.

Thermal conductivity of moderately to highly compacted hemp concretes

The numerical iterative multiscale modeling is here put into practice to estimate the thermal behavior of moderately to highly compacted concretes. This type of concrete is supposed to be transversely isotropic because of the anisotropic behavior of hemp particles combined with their spatial rearrangement in strata during the compaction phase of their elaboration as exhibited by [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF], [START_REF]The influence of the casting process on the internal structure and physical properties of hemp-lime[END_REF]. The global thermal conductivities obtained are all compared to experimental data collected by Nguyen during his Ph.D. and which are partially reported in [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF].

As a first step the numerical iterative multiscale modeling is used to estimate the thermal conductivities of a set of compacted concretes which differ by their formulations (i.e. by the number and volume fractions of their phases), and by their levels of total porosity. It is to be noted that in the literature, concretes formulations are given for a pre-mix state, whereas the simulations presented here require the exact composition after the drying phase. As a consequence the formulation of each concrete of this first set has been identified thanks to inverse methods starting from a measure of the final density of the concrete studied, coupled with an assumption on the distribution of pores in the material. Low density hemp concretes (namely with a density inferior to 500 kg.m -3 ) are here supposed to be three-phased materials constituted of porous lime matrix, porous shives and mesoscopic pores which are approximately the same size as hemp particles; whereas concretes with a higher density (namely with a density superior to 500 kg.m -3 ) are a here considered as a mix of lime and shives only, each with a decreasing porosity with respect to the compaction rate. The decline of intrinsic microporosity in the matrix phase and shives when density increases must be taken into account [START_REF] Walker | Mechanical properties and durability of hemp-lime concretes[END_REF]. It is here achieved thanks to an update of their thermal and mechanical properties following the curves presented on Fig. 7(a). The estimates obtained with the numerical iterative multiscale modeling are reported on Fig. 8. The thermal conductivities at the end of the elaboration phase are estimated in the longitudinal direction of the concretes (i.e. compaction direction) as well as the transverse direction of the concretes (i.e. isotropy or strata planes). The results obtained demonstrate first the ability of the iterative multiscale modeling to account for the geometry of the particles and the anisotropy induced by their morphology and spatial arrangement, an element which had not been tested in the previous non numerical versions of the model. From a quantitative point of view, the values obtained frame the results analytically obtained by Cerezo thanks to a self consistent scheme applied to a material with spherical particles (values added on the graph). For a density close to 400 kg.m -3 the results numerically obtained surround as well the values experimentally obtained on slightly tamped samples regarded as isotropic materials [START_REF] De Bruijn | Moisture fixation and thermal properties of lime-hemp concrete[END_REF]. These values ranged indeed from 0.105 to 0.116 W.m -1 .K -1 . In addition the results obtained by simulation follow the overall trend of the experimental data obtained on anisotropic samples [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF], especially for the lowest densities which correspond in general to the lowest compaction rates. The discrepancies observed here for the formulations with a higher density are therefore attributed to a lack of information concerning the real initial composition of the corresponding concretes after the drying phase. The formulations identified may indeed slightly differ from the exact composition of the experimental samples. As a second step the numerical iterative multiscale modeling has been used to estimate the global thermal properties of a given set of hemp concretes not only after their elaboration but also throughout a compaction phase. An example of the results obtained is reported on Fig. 9. Three levels of compaction are simulated for a given initial formulation. The levels of compaction correspond to the compaction levels for which the properties of the corresponding concretes were experimentally measured [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF]. For each measure, the porosity level has once again been updated with the assumption of a progressive closure of mesoscopic pores followed by a progressive closure of the intrinsic microporosities of the phases [START_REF] Walker | Mechanical properties and durability of hemp-lime concretes[END_REF]. The evolution of the microscopic porosity in the constituents is also accounted for by an update of their properties throughout the simulations, following the non linear curves presented on Fig. 7(a). The agreement with the experimental data is here very satisfactory for both longitudinal and transverse directions. One would also notice that, as expected, the compaction phase whose aim is to increase mechanical properties tends to reduce the insulation efficiency of hemp concretes. The numerical iterative multiscale model could therefore be used on a digital benchmark to help identifying the best compromise between thermal and mechanical properties. Figure 9: Global thermal behavior of a hemp concrete with respect to their density (proportional to compaction rate). Comparison between experimental results [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF] and results obtained with the numerical iterative multiscale modeling.

Elastic rigidity of moderately to highly compacted hemp concretes

In this section, are presented simulations whose aim is to estimate the macroscopic mechanical properties of moderately to highly compacted hemp concretes. Simulations based on the numerical iterative multiscale model are once again performed on a set of concretes which are supposed to have a transverse isotropic global behavior due to the alignment of shives in strata. The formulation of the set of concretes at stake has been priorly estimated thanks to an inverse analysis and thanks to a scenario of pores closure during the compaction phase as it has been done for the estimation of the thermal global properties. The anisotropic behavior of hemp shives described in Section 3.1 is taken into account. Finally, when dealing with the highest compaction rates envisioned (i.e. concretes with the highest densities), the appropriate mechanical properties for the constituents are selected using the results reported on Fig. 7(b).

The results obtained for two specific formulations defined in [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF] are reported on Fig. 10 and are compared to the results experimentally obtained by the corresponding authors. For the lowest densities (i.e. for the lowest compaction rates), the Young modulus obtained for the longitudinal direction (i.e. compaction direction) and the transverse directions (isotropy or strata planes) surround the value statistically obtained from a large collection of samples extracted from batches prepared in numerous independent laboratories [START_REF] Niyigena | Variability of the mechanical properties of hemp concrete[END_REF]. In this study the Young Modulus of hemp concrete treated as an isotropic material ranges from 30 MPa to 40 MPa for a density close to 500 kg.m -3 . For the highest densities the results presented on Fig. 10 show a good concordance between numerical estimates (solid lines) and experimental measures (dotted lines) [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF], and this for both types of formulations Comparison with experimental results by Nguyen [START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF] considered here. These results show thus the ability of the numerical iterative multiscale modeling to account for the global anisotropy of compacted concretes. They also show the necessity to take into account the anisotropic behavior of shives and most of all pore closures in the estimate the behavior for concretes with a high compaction rate.

Conclusion

In this paper was presented an iterative multiscale modeling including finite element simulations on uncluttered meshes allowing to take into account the shapes an orientations of rectangular parallelepipedic particles as well as their influence on the effective global anisotropy of the composites studied. The iterative multiscale modeling has then been put into practice to estimate, in a tridimensional context, the thermal conductivity and elastic rigidity of hemp and lime concretes subjected to a compaction phase during their elaboration. The study of such category of concretes required a preliminary complete inverse identification of the behavior of their constituents in a compacted context since microporosities in shives and lime matrix collapse during the compaction process. This stage was performed thanks to the extended numerical iterative multiscale modeling itself. Simulations were then run to estimate the conductivity and rigidity of moderately and highly compacted concretes microstructures; both of them being transversely isotropic because of a distribution in strata of hemp shives during the compaction phase, and because of the anisotropic behavior of hemp particles. First, the iterative process proved itself efficient to estimate the effective conductivity of a group of concretes with various unrelated formulations and a moderate compaction rate. Then it was used to estimate the effective conductivity and effective rigidity of a smaller set of concretes but for increasing compaction rates. In both cases the results obtained successfully matched experimental data found in the literature. A better precision could nevertheless be obtained thanks to a better identification of the formulations of the composites after the compaction phase and a better experimental identification of the behavior of the phases. Now that the numerical iterative multiscale modeling has been implemented, tested and validated, it needs to be extended in order to simulate the complete non linear behavior of the composites. The non linearity can be of various origins such as thermo and hygromechanics effects, outbreak of microcracks in the matrix phase or the evolution of the microstructure. The evolution of the size and number of porosities, in the course of a loading case has nevertheless already been accounted for in this study via the evolution of the properties of the constituents. The iterative multiscale modeling has formerly been used to describe materials experiencing diffuse isotropic damage as in the work by Vu et al. [START_REF] Vu | A micromechanical numerical modelling approach for the homogenization of grouted sands[END_REF]. The coupling between non linear homogenization methods such as secant method and the iterative method in its numerical version is currently investigated paying ample attention to anisotropy. The results will be communicated in a future paper.

Figure 1 :

 1 Figure 1: Hemp concrete sample and corresponding particles (hemp shives).

Figure 2 :

 2 Figure 2: Basic principle of the iterative homogenization technique.

Figure 3 :

 3 Figure 3: Definition of the RVE and the geometry of the particles used for the resolution of the local problem at each step j.

Figure 4 :

 4 Figure 4: Schematic representation of the iterative addition of particles depending on their families in the digital multiscale modeling. M11 = pristine matrix phase, M ki = intermediary homogeneous equivalent medium at step j = k × i.

11 +

 11 the linear elastic context, the isotropic rigidity tensor C * at the end of a series k and its representative matrix C * are classically expressed as functions of Lamé coefficients λ and µ which are themselves obtained thanks to the components of the intermediate effective rigidity tensor C * 90 = C * (90°, 0°, 0°) as follows : C * 90 22 + C * 90 33 -C * 90 12 -C * 90 13 -

Figure 5 :

 5 Figure 5: Comparison of the global Young modulus of an isotropic random material obtained thanks to the numerical iterative modeling (elongated platty particles randomly distributed) and thanks to analytical solving (spheres).

Figure 6 :

 6 Figure 6: Comparison of the effective properties of two single-oriented composites filled with isotropic or transversally isotropic platy particles. Results obtained by digital simulation with the iterative modeling.

Figure 7 :

 7 Figure7: Transverse isotropic behavior of a hemp particle (shiv) with respect to porosity rate identified thanks to the iterative multiscale modeling (experimental results from Cerezo's Ph.D. work and Samri's master's thesis.).

Figure 8 :

 8 Figure8: Global thermal behavior of hemp concretes with a moderate compaction rate with respect to their density. Comparison between experimental results[START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF] and results obtained with the numerical iterative multiscale modeling as well as an analytical solving with a self-consistent scheme from Cerezo's Ph.D. work.

20

 20

3 1 .K 1 )

 311 E↵ective thermal conductivity K (W.m KLongi Sim. KLongi Exp. KTrans Sim. KTrans Exp.

Figure 10 :

 10 Figure10: Transverse isotropic behavior of two formulations of hemp concretes with respect to their density identified thanks to the numerical iterative multiscale modeling. Comparison with experimental results by Nguyen[START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF]

Table 1 :

 1 Mechanical properties of the phases used for digital validation of the iterative micromechanical modeling.

Table 2 :

 2 Thermal properties of the phases used for digital validation of the iterative micromechanical modeling