Frédéric Albertini

Justin Dirrenberger

Cyrille Sollogoub

Tobias Maconachie

Martin Leary

Andrey Molotnikov

Experimental and computational analysis of the mechanical properties of composite auxetic lattice structures

Keywords:

In this work, the influence of a compliant hyperelastic polymeric phase infiltrated inside stiff auxetic lattices is studied through experimental and numerical approaches. Samples were fabricated using material jetting technology (MJT). The design principle mimics examples of biological materials which combine stiff and compliant materials to attain high superior mechanical properties exceeding the rule of mixtures of both constituent. Two negative Poisson's ratio lattice designs are considered, namely Hexaround and Warmuth cell. Their effective elasto-mechanical properties are investigated through finite element method (FEM) using a homogenization strategy with periodic boundary conditions. A comparison of mechanical properties between lattices and composite lattices, for multiple lattice/matrix volume fractions is discussed and numerical models are validated through a series of compression tests. Results suggest that filling lattices could increase Young's modulus, peak stress, plateau stress and delayed densification of the lattice, hence improving both specific energy absorption (SEA) and absorption efficiency of the considered architectured materials. The improvements are attributed to the presence of the matrix acting as a structural support, modifying lattice failure mode from layerwise to shear band breaking. These results expand the design principles for new energy absorption devices based on architectured materials.

Introduction

Architectured materials are a rising class of advanced materials that open up new opportunities to populate unoccupied areas of Ashby's materials performance maps [START_REF] Ashby | Designing hybrid materials[END_REF] and expand their functional properties. The term architectured materials encompasses any material obtained through a design process that aims to fulfil a specific set of requirements, in terms of functionality, behaviour, or performance, induced by a particular morphology, i.e. the relative topological arrangement between multiple phases, such that some of its materials properties, e.g. yield strength/density, are improved in comparison to those of its constituents, due to structure and composite effects [START_REF] Ashby | Designing hybrid materials[END_REF][START_REF] Bouaziz | Heterogeneous and architectured materials: A possible strategy for design of structural materials[END_REF][START_REF] Bréchet | Architectured materials: Expanding materials space[END_REF][START_REF] Dirrenberger | Towards an integrated approach for the development of architectured materials[END_REF]. Among novel properties associated with a special shape are auxetic materials, which are considered as promising candidate for future engineering applications [START_REF] Lakes | Foam structures with a negative Poisson's ratio[END_REF][START_REF] Lakes | Deformation mechanisms in negative Poisson's ratio materials: structural aspects[END_REF][START_REF] Milton | Composite materials with Poisson's ratios close to -1[END_REF][START_REF] Prall | Properties of a chiral honeycomb with a Poisson's ratio of -1[END_REF][START_REF] Scarpa | Dynamic crushing of auxetic open-cell polyurethane foam[END_REF][START_REF] Yang | Review on auxetic materials[END_REF][START_REF] Spadoni | Phononic properties of hexagonal chiral lattices[END_REF][START_REF] Alderson | Elastic constants of 3-, 4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[END_REF][START_REF] Dirrenberger | Homogenization of periodic auxetic materials[END_REF][START_REF] Pasternak | Materials and structures with macroscopic negative Poisson's ratio[END_REF][START_REF] Alvarez Elipe | Comparative study of auxetic geometries by means of computer-aided design and engineering[END_REF][START_REF] Dirrenberger | Elastoplasticity of auxetic materials[END_REF][START_REF] Dirrenberger | Effective elastic properties of auxetic microstructures: anisotropy and structural applications[END_REF][START_REF] Kaminakis | Design and verification of auxetic microstructures using topology optimization and homogenization[END_REF][START_REF] Körner | A systematic approach to identify cellular auxetic materials[END_REF][START_REF] Saxena | Three decades of auxetics research-materials with negative Poisson's ratio: a review[END_REF][START_REF] Wang | Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization[END_REF][START_REF] Karathanasopoulos | Designing two-dimensional metamaterials of controlled static and dynamic properties[END_REF][START_REF] Karathanasopoulos | Computing the effective bulk and normal to shear properties of common two-dimensional architectured materials[END_REF][START_REF] Wang | Systematic design of tetra-petals auxetic structures with stiffness constraint[END_REF].

Auxetics designate a group of architectured materials that exhibit negative Poisson's ratio. Such property implies that auxetics expand transversely when stretched, and shrink when compressed, contrary to conventional materials. In the case of three-dimensional isotropic elasticity, Poisson's ratio 𝜈 is ranging from -1 (unshearable) to 0.5 (incompressible, rubber-like). However, most known natural and engineered materials exhibit a positive Poisson's ratio. Studies about auxetic behaviour started in the 80's [START_REF] Lakes | Foam structures with a negative Poisson's ratio[END_REF][START_REF] Herakovich | Composite laminates with negative through-the-thickness Poisson's ratios[END_REF][START_REF] Almgren | An isotropic three-dimensional structure with Poisson's ratio=-1[END_REF], drawing increasing attention since then [START_REF] Lakes | Deformation mechanisms in negative Poisson's ratio materials: structural aspects[END_REF][START_REF] Milton | Composite materials with Poisson's ratios close to -1[END_REF][START_REF] Prall | Properties of a chiral honeycomb with a Poisson's ratio of -1[END_REF][START_REF] Yang | Review on auxetic materials[END_REF][START_REF] Alderson | Elastic constants of 3-, 4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[END_REF][START_REF] Dirrenberger | Homogenization of periodic auxetic materials[END_REF][START_REF] Pasternak | Materials and structures with macroscopic negative Poisson's ratio[END_REF][START_REF] Alvarez Elipe | Comparative study of auxetic geometries by means of computer-aided design and engineering[END_REF][START_REF] Dirrenberger | Elastoplasticity of auxetic materials[END_REF][START_REF] Dirrenberger | Effective elastic properties of auxetic microstructures: anisotropy and structural applications[END_REF][START_REF] Kaminakis | Design and verification of auxetic microstructures using topology optimization and homogenization[END_REF][START_REF] Körner | A systematic approach to identify cellular auxetic materials[END_REF][START_REF] Bathurst | Note on a random isotropic granular material with negative Poisson's ratio[END_REF][START_REF] Caddock | Microporous materials with negative Poisson's ratios: I. Microstructure and mechanical properties[END_REF][START_REF] Hughes | Auxetic frameworks inspired by cubic crystals[END_REF]. Reported properties of negative Poisson's ratio materials cover a large spectrum of applications, including acoustic damping [START_REF] Lipsett | Reexamination of dynamic problems of elasticity for negative Poisson's ratio[END_REF], improved indentation resistance compared to conventional cellular materials [START_REF] Dirrenberger | Effective elastic properties of auxetic microstructures: anisotropy and structural applications[END_REF][START_REF] Chan | Indentation resilience of conventional and auxetic foams[END_REF], improved fracture toughness [START_REF] Choi | Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis[END_REF], or as wave-guiding medium [START_REF] Spadoni | Phononic properties of hexagonal chiral lattices[END_REF][START_REF] Rosi | Anisotropic and dispersive wave propagation within strain-gradient framework[END_REF]. Recently, the auxetics have been explored as an energy absorbing medium in order to improve crashworthiness [START_REF] Scarpa | Dynamic crushing of auxetic open-cell polyurethane foam[END_REF][START_REF] Liu | In-plane dynamic crushing of re-entrant auxetic cellular structure[END_REF][START_REF] Li | Exploiting negative Poisson's ratio to design 3d-printed composites with enhanced mechanical properties[END_REF][START_REF] Novak | Blast response study of the sandwich composite panels with 3d chiral auxetic core[END_REF]. While typically metals or composite materials are used to absorb energy either due to plastic deformation [START_REF] Kim | Crashworthiness of aluminum/cfrp square hollow section beam under axial impact loading for crash box application[END_REF] or complex failure modes [START_REF] Maskery | Compressive failure modes and energy absorption in additively manufactured double gyroid lattices[END_REF], much less attention is given to the morphology of the parts. Often rectangular boxes or axial tubes are utilized due to the ease of manufacturing. However, the use of hybrid or composite materials and selective placement of materials in a part could further enhance the energy absorption capability of these new materials. Ashby and Bréchet [START_REF] Ashby | Designing hybrid materials[END_REF] defined hybrids as ''the combination of two (or more) existing materials so as to allow a superposition of their properties''. This definition encompasses many strategies to produce a E-mail addresses: justin.dirrenberger@ensam.eu (J. Dirrenberger), andrey.molotnikov@rmit.edu.au (A. Molotnikov). https://doi.org/10.1016/j.addma.2021.102351 hybrid material including combination of architectured materials with monolithic ones, referred in this paper as multi-material architectured material. Multi-material architectured materials aim at combining the benefits from architecture, e.g. lightweight with superior mechanical properties, with those of monolithic materials. It is hypothesized that crashworthiness can be tailored by combining ''stiff and compliant'' material which is the focus of the present work.

Examples of architectured materials that associate stiff and compliant materials can be found in numerous biological materials. The well-studied brick-and-mortar structure of nacre [START_REF] Luz | Biomimetic design of materials and biomaterials inspired by the structure of nacre[END_REF][START_REF] Wegst | Bioinspired structural materials[END_REF][START_REF] Yin | Tough and deformable glasses with bioinspired cross-ply architectures[END_REF][START_REF] Yin | Impact-resistant nacre-like transparent materials[END_REF], exhibit high strength and toughness, far exceeding the properties of its constituents. Another example is turtle shell which consists of the assembly of stiff scales joined by compliant interfaces, providing flexibility under small deformations, but high stiffness under larger deformations [START_REF] Krauss | Mechanical function of a complex three-dimensional suture joining the bony elements in the shell of the red-ear ed slider turtle[END_REF][START_REF] Dunlop | Artful interfaces within biological materials[END_REF]. Among stiff/compliant engineered architectured materials, one can cite stochastic composites, as fibrous composites [START_REF] Schaefer | Carbon nanofibre reinforcement of soft materials[END_REF][START_REF] Dirrenberger | Towards gigantic RVE sizes for stochastic fibrous networks[END_REF] that confer high stiffness for reduced mass, particulate composites [START_REF] Bapari | The role of the soft phase in rigidity enhancements in a particulate composite[END_REF] increasing stiffness through percolation, or composite metallic foams [START_REF] Kwon | Representative unit-cell models for opencell metal foams with or without elastic filler[END_REF][START_REF] Liu | Mechanical behavior of aluminum foam/polyurethane interpenetrating phase composites under monotonic and cyclic compression[END_REF] that present increased stiffness, yield stress and dissipated energy compared to simple lattices.

Recently, advances in additive manufacturing technologies (especially resolution and availability to combine multiple materials in the same build) opened up a possibility of manufacturing deterministic composites, such as Interpenetrated Phase Composites (IPC) [START_REF] Al-Ketan | Mechanical properties of a new type of architected interpenetrating phase composite materials[END_REF][START_REF] Al-Ketan | Mechanical properties of periodic interpenetrating phase composites with novel architected microstructures[END_REF] or 2D composite structures [START_REF] Li | Exploiting negative Poisson's ratio to design 3d-printed composites with enhanced mechanical properties[END_REF][START_REF] Murray | Auxetic honeycombs with lossy polymeric infills for high damping structural materials[END_REF][START_REF] Fíla | Impact testing of polymer-filled auxetics using split hopkinson pressure bar[END_REF] that all report increased stiffness, yield stress and dissipated energy compared to single material structures. Combination of stochastic foams with lattice structures have also been investigated in [START_REF] Bernal Ostos | Deformation stabilization of lattice structures via foam addition[END_REF], showing that foam addition stabilizes lattices from buckling, therefore increasing post-buckling strength and exhibiting energy absorption capacity higher than that of both components taken separately.

Fewer studies focused on the combination of hard lattice structures with compliant hyperelastic materials [START_REF] Novak | Mechanical properties of hybrid metamaterial with auxetic chiral cellular structure and silicon filler[END_REF][START_REF] Xue | Enhanced compressive mechanical properties of aluminum based auxetic lattice structures filled with polymers[END_REF]. For instance, in the study by Novak et al. [START_REF] Novak | Mechanical properties of hybrid metamaterial with auxetic chiral cellular structure and silicon filler[END_REF], auxetic metallic lattices are filled with silicone and it was demonstrated that these composites have a higher elastic modulus and improved compressive strength. However, the study did not investigate the influence of volume fraction and elastic properties of the constitutive phases on the mechanical properties.

Previous studies have also numerically investigated the effect of filling lattices with soft materials and shown its influences on the auxetic properties [START_REF] Strek | Computational design of two-phase auxetic structures[END_REF][START_REF] Jopek | Finite element analysis of tunable composite tubes reinforced with auxetic structures[END_REF][START_REF] Jopek | Thermoauxetic behavior of composite structures[END_REF][START_REF] Peng | Phase contrast mediated switch of auxetic mechanism in composites of infilled re-entrant honeycomb microstructures[END_REF][START_REF] Zhang | Auxetic interpenetrating composites: A new approach to non-porous materials with a negative or zero Poisson's ratio[END_REF]. In other studies, it was reported that it can lead to a delayed buckling of struts and postponement of densification and failure and therefore increasing the elastic modulus and peak stress [START_REF] Fíla | Impact testing of polymer-filled auxetics using split hopkinson pressure bar[END_REF][START_REF] Novak | Mechanical properties of hybrid metamaterial with auxetic chiral cellular structure and silicon filler[END_REF][START_REF] Xue | Enhanced compressive mechanical properties of aluminum based auxetic lattice structures filled with polymers[END_REF][START_REF] Li | Metallic microlattice and epoxy interpenetrating phase composites: Experimental and simulation studies on superior mechanical properties and their mechanisms[END_REF].

In this work, we study the influence of a compliant hyperelastic polymeric phase infiltrated inside stiff auxetic lattices. Specifically, two different auxetic lattices, namely Hexaround [START_REF] Albertini | Computational investigation of the effective mechanical behavior for 3D pre-buckled auxetic lattices[END_REF] and cubic antichiral [START_REF] Warmuth | Single phase 3d phononic band gap material[END_REF] (referred to as Warmuth cell in this work) are designed and manufactured using Polyjet technology. Firstly, we will investigate the effect of elastomeric filling on the elastic behaviour of lattices by the means of computational homogenization. Secondly, finite element simulation based on a finite-strain framework will be performed in order to address the nonlinear mechanical behaviour of auxetic lattices, and compare these results to mechanical tests are performed on additively manufactured samples.

Nomenclature

Throughout this work, the following notation is used: 𝑥 for scalars, 𝑥 for vectors, 𝒙 ∼ for 2nd-order tensors, 𝒙 ∼ ∼ for 4th-order tensors, ⋅ for dot product, ∶ for doubly-contracted dot product, ⟨𝑥⟩ for spatial average, and x for ensemble average.

Experimental procedures

Design of auxetic composite lattice structure

In this work, two types of lattice unit cells are selected due to their ability to show auxetic behaviour, see Figs. 1(a) and 1(b). The Hexaround geometry was proposed by some of the coauthors of the present paper in [START_REF] Albertini | Computational investigation of the effective mechanical behavior for 3D pre-buckled auxetic lattices[END_REF], while the Warmuth cell is a well-known lattice cell with both computational [START_REF] Warmuth | Single phase 3d phononic band gap material[END_REF] and experimental [START_REF] Warmuth | Fabrication and characterisation of a fully auxetic 3d lattice structure via selective electron beam melting[END_REF] data available, making it an adequate point of comparison. Unit-cells have been generated using Rhinoceros 3D1 with the Grasshopper plug-in. The obtained CAD files were exported to STEP and STL files to be used for finite element (FE) modelling and additive manufacturing. Unit-cells are described with respect to geometrical parameters. In the present study, side length of the cubic unit-cells has been chosen equal for both cells, as well as waviness amplitude, for comparison purpose. Only diameter of struts differs, so that each unit-cells could be compared at the same volume fraction 𝜌 * , as defined by Eq. [START_REF] Dirrenberger | Homogenization of periodic auxetic materials[END_REF].

A full description of the Hexaround cell is given in [START_REF] Albertini | Computational investigation of the effective mechanical behavior for 3D pre-buckled auxetic lattices[END_REF]. Struts of the cell are arc-shaped, and negative Poisson ratio (PR) is achieved through inward orientation of arcs. It can be described using 3 parameters: 𝐿, side length of the cubic cell, 𝑎, waviness amplitude, and 𝐷, diameter of the struts (see Fig. 1). The different sets of geometrical parameters result in volume fraction that are displayed in Table 1.

Similarly, the Warmuth cell is generated using the 13th eigen-mode of the regular cubic unit-cell as described in [START_REF] Warmuth | Fabrication and characterisation of a fully auxetic 3d lattice structure via selective electron beam melting[END_REF] and [START_REF] Körner | A systematic approach to identify cellular auxetic materials[END_REF]. The struts are sinusoidal with a circular cross-section. It can be described using 3 parameters: 𝐿, side length of the cubic cell, 𝑎, the amplitude of sine, and 𝐷, diameter of the struts (see Fig. 1b). The different sets of geometrical parameters result in volume fraction that are displayed in Table 2.

Once the lattice structure are defined, their composite counterpart is obtained by filling the voids in the geometry with a soft polymer, see Fig. 1(c).

Materials and methods

Samples have been manufactured using a Stratasys Connex Ob-jet350 printer (multi-material Polyjet material jetting technology). Polyjet technology is based on a liquid droplet deposition method, it can achieve a printing resolution of 600 dpi in both the X-and Y-axes, 1600 dpi in the 𝑍-axis, and a minimum layer thickness of 16 μm [67]. Recent studies have shown its ability to manufacture multi-material composites in a single process [START_REF] Loh | An overview of functionally graded additive manufacturing[END_REF][START_REF] Tee | 3d printing of polymer composites with material jetting: Mechanical and fractographic analysis[END_REF] as matrix. Such materials have been used to produce triply periodic minimal surface-based Interpenetrated Phase Composites [START_REF] Al-Ketan | Mechanical properties of a new type of architected interpenetrating phase composite materials[END_REF][START_REF] Al-Ketan | Mechanical properties of periodic interpenetrating phase composites with novel architected microstructures[END_REF] or topological interlocking structures [START_REF] Djumas | Deformation mechanics of nonplanar topologically interlocked assemblies with structural hierarchy and varying geometry[END_REF]. A full factorial experiment is made, using a total of 16 samples, 4 repetitions of each lattice design and type (Hexaround/Warmuth; lattice/composite lattices). Each sample consists of a cube of 5 unit-cells per side, corresponding to a 30*30*30 mm cube, as can be seen on Fig. 2.

VeroWhite is used as constituent for the stiff lattice phase. It's behaviour is considered elasto-plastic, and can be modelled through an isotropic non-linear hardening model [START_REF] Viard | Propagating material instabilities in planar architectured materials[END_REF], given by Eq. ( 1):

𝑅 = 𝑅 0 + 3 ∑ 𝑖 𝑄 𝑖 (1 -𝑒 -𝑏 𝑖 𝑝 ) (1)
Material parameters of VeroWhite's model have been identified from tensile testings (see Fig. 3 TangoBlack+ is used as the compliant phase. Its behaviour is hyperelastic and have been modelled using the Arruda-Boyce model [START_REF] Arruda | A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials[END_REF]. Fitting experimental results from tensile testings, following parameters of A-B model has been identified (see Fig. A separate study was undertaken to investigate the manufacturability of these composite structures and it was shown that lattices with 20% volume fraction could be manufactured reliably and will be used for the validation of the proposed numerical methods. Due to the nature of Polyjet 3D material jetting process, all lattice samples were filled with support material (a water soluble, wax-like material) that needed to be removed before testing. All lattices were cleaned in an ultrasonic bath with heated solution of caustic soda (5% in concentration), for half an hour, before being rinsed using water jet in order to remove the support material. On the other hand, the composite lattices only required a surface cleaning.

Manufactured samples have been weighed to compare with theoretical weights obtained from CAD designs. The measured weights are shown in Table 3. It can be seen that the manufactured lattices and composites are slightly heavier than the theoretically calculated values based on CAD files which is associated with manufacturing spatial accuracy, and minor absorption of moisture from water and environment due to the cleaning process.

Experimental testing

Mechanical behaviour of both manufactured lattice and composite samples has been investigated through compressive tests. An Instron 5969 tensile machine with a 50 kN load cell was used, plates being lubricated in order to reduce friction, using ''Super Lube'' grease. The applied strain rate was 0.001/s, corresponding to a displacement speed of the plate of 1.8 mm/min. Strain was calculated using recorded plate displacement. Average stress 𝜎 have been computed as the applied load 𝐹 divided by sample cross section 𝑆 = (5.𝐿).(5.𝐿), with S = 900 mm 2 in our case.

Computational homogenization

In this work, computational homogenization is used to predict the effective elastic properties of lattices and composites.

CAD files (STEP format) are meshed using GMSH software [START_REF] Geuzaine | Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities[END_REF] with tetrahedral quadratic elements (C3D10). FE analysis has been conducted using Z-Set FE package. 2 A mesh sensitivity study has been performed to ensure numerical accuracy, and is presented in Appendix A.

2 http://www.zset-software.com.

By computing the volume averaged response under a physical stimulus over a virtual sample that is considered a representative volume element (RVE), one can identify the effective properties of a heterogeneous medium [START_REF] Jeulin | Caractérisation Morphologique et Modèles de Structures Aléatoires[END_REF][START_REF] Torquato | Random Heterogeneous Materials[END_REF][START_REF] Assidi | Composites with auxetic inclusions showing both an auxetic behavior and enhancement of their mechanical properties[END_REF][START_REF] Nady | Computation of the homogenized nonlinear elastic response of 2d and 3d auxetic structures based on micropolar continuum models[END_REF][START_REF] Dirrenberger | Computational homogenization of architectured materials[END_REF].

Considering the small deformation hypothesis, constitutive relations are expressed locally in a linear elasticity framework using the generalized Hooke law:

𝝈 ∼ (𝑥) = 𝒄 ∼ ∼ (𝑥) ∶ 𝝃 ∼ (𝑥) (2)
with 𝝈 ∼ second-order symmetric Cauchy stress tensor, 𝝃 ∼ second-order symmetric engineering strain tensor, and 𝒄 ∼ ∼ fourth-order positive definite tensor of elastic moduli. Considering a volume element 𝑉 , the macroscopic stress and strain tensors 𝜮 ∼ and 𝜩 ∼ are defined by the spatial averages over 𝑉 of local stress 𝝈 ∼ and strain 𝝃 ∼ fields.

𝜮 ∼ ∶= ⟨𝝈 ∼ ⟩ = 1 𝑉 ∫ 𝑉 𝝈 ∼ 𝑑𝑉 ( 3
)
𝜩 ∼ ∶= ⟨𝝃 ∼ ⟩ = 1 𝑉 ∫ 𝑉 𝝃 ∼ 𝑑𝑉 (4)
From Eqs. ( 2)-( 4), it yields the tensor of effective elastic moduli 𝑪 ∼ ∼ :

𝜮 ∼ = 𝑪 ∼ ∼ ∶ 𝜩 ∼ (5)
For periodic boundary conditions, the displacement field 𝑢 can be dissociated into a part given by the macroscopic strain tensor 𝜩 ∼ and a periodic fluctuation field 𝑣 for any material point 𝑥 of 𝑉 , such that:

𝑢 = 𝜩 ∼ ⋅ 𝑥 + 𝑣 ∀𝑥 ∈ 𝑉 (6)
with 𝑣 the periodic fluctuations vector, i.e. taking the same value on two homologous points 𝑥 + and 𝑥 -of the domain boundary 𝜕𝑉 . Furthermore, in order to ensure static equilibrium, the traction vector 𝑡 = 𝝈 ∼ ⋅ 𝑛 fulfilled antiperiodic conditions, considering 𝑛 the vector normal to any point 𝑥 ∈ 𝜕𝑉 such that,

𝝈 ∼ + ⋅ 𝑛 + + 𝝈 ∼ -⋅ 𝑛 -= 0 (7) 𝑣 + -𝑣 -= 0 (8)
The elastic moduli tensor 𝑪 ∼ ∼ can then be fully identified by applying successively 6 fundamental macroscopic loading, i.e. 3 pure extensions, and 3 pure shears. Although not all needed since the Hexaround cell exhibits a cubic symmetry, and the Warmuth cell an orthotropic one, the 6 independent computations are run since the developed methodology is generic and automated. The elastic moduli tensor is identified by applying the macroscopic strain 𝜩 ∼ , and measuring the corresponding macroscopic stress components. Using Voigt's notation, here is an example for cubic elasticity:

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 𝛴 11 𝛴 22 𝛴 33 𝛴 23 𝛴 31 𝛴 12 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 𝐶 11 𝐶 12 𝐶 12 0 0 0 𝐶 12 𝐶 11 𝐶 12 0 0 0 𝐶 12 𝐶 12 𝐶 11 0 0 0 0 0 0 𝐶 44 0 0 0 0 0 0 𝐶 44 0 0 0 0 0 0 𝐶 44 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 𝐸 11 𝐸 22 𝐸 33 2𝐸 23 2𝐸 31 2𝐸 12 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (9)
Using the identified stiffness tensor, one can compute elastic properties of the cell in every spatial direction. Here, Euler-Bunge [START_REF] Bunge | Texture Analysis in Materials Science[END_REF] angles 𝜙, 𝜃, and 𝜓, have been used to define 3 orthogonal vectors 𝑙, 𝑚, and 𝑛, as shown on Fig. 4.

Using the macroscopic stress 𝜮 ∼ (𝜙, 𝜃, 𝜓) and strain 𝜩 ∼ (𝜙, 𝜃, 𝜓) tensors, effective Young's modulus 𝐸 ( 𝑙 ) and Poisson's ratio 𝜈 * (𝑙, 𝑚) are defined as follows: Finally, the normalized modulus of cellular and architectured materials can be defined with respect to its constitutive material Young's modulus 𝐸 0 , and its volume fraction 𝑉 𝑓 :

𝐸 = 𝑙 ⋅ 𝜮 ∼ ⋅ 𝑙 𝑙 ⋅ 𝜩 ∼ ⋅ 𝑙 ( 10
)
𝜈 * = - 𝑚 ⋅ 𝜩 ∼ ⋅ 𝑚 𝑙 ⋅ 𝜩 ∼ ⋅ 𝑙 (11)
𝐸 * = 1 𝐸 0 𝑉 𝑓 𝐸 ( 12
)
volume fraction 𝑉 𝑓 being defined as the volume occupied by a periodic cell 𝑉 lattice divided by the cubic volume circumscribed by the cell (𝑉 cubic = 𝐿3 ) as shown on Fig. 5.

𝑉 𝑓 =

𝑉 lattice 𝑉 cubic (13)

Computational experiments

In addition to computational homogenization of elastic properties for the lattices, a full-field finite element simulation using nonlinear material models within a finite deformation framework. The objective here is to simulate the compression experiments for comparison. The stress measured is the Boussinesq or 1st Piola-Kirchhoff stress, while the corresponding strain measure is the Green-Lagrange strain. Computations are performed on unit-cells, applying periodic boundary conditions and prescribing macroscopic uniaxial strain component. The choice of working on a periodic unit-cell instead of the full sample geometry is driven by the computational cost of such calculation, which is already very intensive, e.g. 1.2 million degrees of freedom for a composite lattice unit-cell, taking up to 100 h of computation running on a Intel Xeon E5-2640 v4 CPU at 2.4 GHz using 8 cores and 180 GB of RAM. All simulations are performed using tetrahedral quadratic elements (C3D10) and their sizes were determined using mesh convergence analysis, that can be found in Appendix A. The implicit solver MUMPS 3 (MUltifrontal Massively Parallel Solver) is used. Materials behaviour is identified from experimental curves shown in Fig. 3, as presented in Section 2.2. In the context of the present work, no damage was considered in the modelling. This will be the focus a forthcoming paper.

Results and discussions

Computational homogenization of elastic properties

In this section, a comparison of numerically computed effective elastic properties (normalized Young's modulus 𝐸 * and Poisson's ratio 𝜈 in this study) with and without compliant matrix is made. Numerical results have been obtained through homogenization for different volume fraction of the presented unit-cells, only varying the diameter of the struts 𝐷 to generate five different volume fraction values 𝑉 𝑓 : [5, 10, 15, 20, 25%].

In order to compute the elastic properties, the behaviour of both constitutive materials is considered purely elastic isotropic using experimentally identified properties displayed in Table 4.

Normalized modulus

Normalized modulus have been computed for both lattices and composite lattices, plotted in (0,0, 𝜓) plan, with regards to the volume fraction of lattices. As both lattices exhibit cubic elastic behavioureven the Warmuth cell which is not properly cubic from a geometrical viewpoint -only 1/4 of the plane is represented (𝜓 is taken between 0 and 90 • ). A complete 3D map for elastic stiffness of lattices is given in Appendix B. Normalized modulus for both lattice design are displayed in Fig. 6(a) and(c). Normalized volume fractions are obtained by varying the lattice strut diameter, while maintaining waviness amplitude and cell size. The composite lattices normalized modulus is computed considering a rule of mixture for constitutive material 𝐸 0 . This corresponds to a theoretical maximum value for composites, hence making it adequate for normalizing the results: [START_REF] Pasternak | Materials and structures with macroscopic negative Poisson's ratio[END_REF] with 𝐸 𝑉 𝑊 and 𝐸 𝑇 𝐵+ , respectively the Young moduli of VeroWhite and TangoBlack+ phases, as presented in Table 4. Evolution of Hexaround normalized modulus depending on the loading orientation is presented on Fig. 6(a). It shows that on the plane (0,0, 𝜓), maximum normalized modulus is obtained for 𝜓 = 45 • , for all densities. Maximum normalized modulus for Hexaround lattice is 𝐸 * = 0.058 at 𝑉 𝑓 = 5%, and 𝐸 * = 0.243 at 𝑉 𝑓 = 25%, respectively. The composite Hexaround lattices show a maximum normalized modulus of 𝐸 * = 0.167 at 𝑉 𝑓 = 5%, and 𝐸 * = 0.250 at 𝑉 𝑓 = 25%. It is noteworthy that the maximum value of normalized modulus for the Hexaround cell is not found in the plane (0,0, 𝜓) but rather in (0, 𝜋 4 , 𝜓), along [111] loading orientation as reported in [START_REF] Albertini | Computational investigation of the effective mechanical behavior for 3D pre-buckled auxetic lattices[END_REF].

𝐸 0 = 𝑉 𝑓 .𝐸 𝑉 𝑊 + (1 -𝑉 𝑓 ).𝐸 𝑇 𝐵+
Evolution of Warmuth normalized modulus depending on the loading orientation is presented on Fig. 6(c). It shows that on the plane (0,0, 𝜓), maximal normalized modulus is obtained for 𝜓 = 0 • (mod 90 • ) [START_REF] Warmuth | Fabrication and characterisation of a fully auxetic 3d lattice structure via selective electron beam melting[END_REF] at all volume fractions. Maximal normalized modulus for Warmuth lattice is 𝐸 * = 0.009 at 𝑉 𝑓 = 5%, and 𝐸 * = 0.053 at 𝑉 𝑓 = 25%. Concerning Warmuth composite lattices, maximal normalized modulus is 𝐸 * = 0.030 at 𝑉 𝑓 = 5%, and 𝐸 * = 0.059 at 𝑉 𝑓 = 25%.

Influence of filling on normalized modulus

Results show that adding a compliant filling material inside lattices has the obvious effect of stiffening them. However, the stiffening effect seems not only affected by modulus of both phase, but also by the volume fraction distribution between lattice and matrix. It can be seen on Fig. 7(a) and (c) that the filling influence is decreasing with the increase of lattice volume fraction 𝑉 𝑓 . At 𝑉 𝑓 = 0.05, Hexaround normalized modulus increase by 198%, but at 𝑉 𝑓 = 0.25 it only increase by 3%. The same trend is observed with Warmuth lattice, suggesting that the modulus ratio between compliant (matrix) and stiff phase (lattice) is critical. Consequence is that filling a lattice may present low influence on its normalized Young's modulus if the lattice is too stiff compared to the filling material, as can be seen for the Hexaround lattice at 25% volume fraction.

Poisson's ratio

Poisson's ratio (PR) of both lattices and composites have been evaluated in plane containing their minimal values, as reported in [START_REF] Albertini | Computational investigation of the effective mechanical behavior for 3D pre-buckled auxetic lattices[END_REF] and [START_REF] Warmuth | Fabrication and characterisation of a fully auxetic 3d lattice structure via selective electron beam melting[END_REF], i.e. the (0,0, 𝜓) plan, for each design regarding lattice volume fraction. As for the modulus, only 1/4 of the plane is represented due to the elastic moduli tensor symmetry. PR of both lattice designs are displayed in Fig. 6(b) and(d).

Evolution of Hexaround PR depending on the loading orientation is presented on Fig. 6(b). It shows that on the plane (0,0, 𝜓), minimal PR is reached for 𝜓 = 45 • for all volume fractions. Minimal PR for Hexaround lattice is 𝜈 * = -0.60 at 𝑉 𝑓 = 5%, and 𝜈 * = -0.01 at 𝑉 𝑓 = 25%. Concerning Hexaround composite lattices, minimal PR is 𝜈 * = -0.01 at 𝑉 𝑓 = 5%, and 𝜈 * = 0.04 at 𝑉 𝑓 = 25%. As can be seen on Fig. 7(b), incorporating a soft phase into a rigid lattice structure shows a non-monotonic influence over Hexaround PR, but it's influence is decreasing with the increase of lattice volume fraction 𝑉 𝑓 .

Evolution of Warmuth PR depending on the loading orientation is presented on Fig. 6(d). It shows that on the plane (0,0, 𝜓), minimal PR is found for 𝜓 = 0 • (mod 90 • ) at all volume fractions. Minimal PR for Warmuth lattice is 𝜈 * = -0.35 at 𝑉 𝑓 = 5%, and 𝜈 * = -0.32 at 𝑉 𝑓 = 25%. Concerning Warmuth composite lattices, minimal PR is 𝜈 * = 0.44 at 𝑉 𝑓 = 5%, and 𝜈 * = -0.20 at 𝑉 𝑓 = 25%. In contrast to Hexaround structure incorporation of a soft phase into the Warmuth lattice structure strongly increases Warmuth PR at low volume fraction, but it's influence is decreasing while lattice volume fraction 𝑉 𝑓 increases.

Influence of filling on Poisson's ratio

One can observe on Fig. 7(b) and (d) that filling increases Poisson's ratio value, making it closer to TangoBlack+ and thus reducing auxeticity of the lattices. It can be explained by the presence of the elastomer that hinders the deformation of the lattice. However, the influence of the filling is non-monotonic. A strong influence of lattice volume fraction can be observed: the higher the lattice volume fraction, the lesser the effect of filling on Poisson's ratio.

Compression tests

Results of compression tests are presented on Fig. 10, displaying lattice, composite lattices and pure TangoBlack+ stress/strain curves. Compression plates were lubricated in order to minimize friction in both simple lattice and composite lattice during the compression tests. In order to make a relevant comparison, TB+ curve is a FE compression simulation of a TB+ cube of same dimensions as experimental composite samples are compared. TB+ behaviour used for simulations was identified from experimental testings, shown in Fig. 3. The complete experimental records are displayed in Appendix C. These results are compared with those from the corresponding computational experiment.

Hexaround cell

Hexaround lattices present a layerwise failure, each bump corresponding to the collapse of one floor. The average peak stress is 0.83 MPa, average densification occurs at 47% strain. The average measured Young's modulus is 22.15 MPa. Hexaround composite lattices compression test begins with a linear part with an average measured Young's modulus of 31.04 MPa, followed by plastic deformation and failure of the lattice due to the formation of shear band. An average peak stress of 2.63 MPa is reached, then densification occurs at 65% strain. It can be seen on Fig. 8 that the composite lattice displays very different behaviour and instead of layerwise failure a shear band formation and failure is observed. This difference can be explained by the presence of the matrix that prevents the lattice to collapse layerwise, delaying deformation of the struts and distributing stress more evenly as shown by FE simulations in Fig. 9. Average peak stress is increased from 0.83 to 2.63 MPa (a 217% increase), and densification is delayed from an average 47% to 65% strain. Measured Young's modulus is increased by 40%.

Warmuth cell

Warmuth lattice compression behaviour starts with a linear elastic part, followed by a plateau. Damage occurs resulting in stress peaks until densification. An average peak stress of 0.58 MPa is reached and densification occurs around 49% strain. From the linear elastic part, the average measured Young's modulus is 3.75 MPa. Composite lattices compression behaviour begins with a small linear part until 2.5% strain, followed by non-linear elasticity. Plateau, damage and densification followed. An average peak stress of 2.83 MPa is reached, then densification occurs at an approximate 61% strain. Average measured Young's modulus is 19.05 MPa. For this design, peak stress is increased from 0.58 to 2.83 MPa (a 388% increase), and densification is delayed from 49% to 61% strain. Average measured Young's modulus is increased by 400%.

The influence of filling with a compliant phase on the Warmuth lattice mechanical properties has a more important effect compared to that of Hexaround composite lattice structure. This observation can be explained by the fact that Warmuth lattice properties are lower than the Hexaround, being 5.9 times more compliant. Therefore it can be concluded that the lower the lattice base modulus, the greatest the increase of mechanical properties due to filling strategy. Table 5 provides a comparison of mechanical properties for all samples. Simulation is yielding an overestimation of the mechanical response for the lattices, due to defect-free nature of the computational samples, contrary to the actual experimental samples that were obtained through additive manufacturing. The small discrepancies between computational experiments and computational homogenization regarding the value of 𝐸 is due to the nonlinear nature of the matrix phase, which is not taken into account properly in the computational homogenization scheme, due to the linear hypothesis.

Crashworthiness evaluation

The crashworthiness properties of lattices and composite lattices are compared using the Specific Energy Absorption (SEA). This experimental measure is considered a reliable indicator to compare the Energy Absorption (EA) with regard to the weight of the samples. EA is calculated as the area under stress-strain curves, yielding a mechanical work density, depending on the uniaxial strain 𝜉 and principal stress measure 𝜎 in the following manner:

𝐸𝐴(𝜉) = ∫ 𝜉 0 𝜎(𝜉) d𝜉 (15)
SEA is defined as the sum of the energy density dissipated and elastic energy density stored in the sample volume until densification, divided by the mass of the sample, 𝑚. Densification happens when cell struts reach contact with one another, and is achieved when peak stress value is reached a second time. Thus, SEA is expressed in J g -1 cm -3 , and can be calculated such that:

𝑆𝐸𝐴 = 1 𝑚 ∫ 𝜉 𝑑 0 𝜎(𝜉) d𝜉 (16)
VeroWhite and TangoBlack+ having very close density (respectively 1.175 g cm -3 and 1.141 g cm -3 ), and the lattice volume fraction being 𝑉 𝑓 = 20%, one can infer that composite lattices are approximately 5 times heavier than lattices samples. Thus in order to dissipate more energy than the lattice, composite lattices must at least dissipate 5 times more energy.

Another pertinent criterion is the absorption efficiency 𝜂, expressed in Eq. [START_REF] Dirrenberger | Effective elastic properties of auxetic microstructures: anisotropy and structural applications[END_REF]. It may be used to compare the efficiency of lattices and composite lattices, with regards to idealized absorber in the case of a total uniaxial strain 𝜉 of 100%.

𝜂 = ∫ 𝜉 𝑑 0 𝜎(𝜉) d𝜉 𝜎 𝑝𝑒𝑎𝑘 .1 (17)
Both energy criteria have been plotted on Fig. 11, with Hexaround SEA and absorption efficiency on the left, and Warmuth ones on the right.

Hexaround cell

Despite the fact that composite Hexaround lattices exhibit higher stiffness and yield stress than simple ones, it can be seen in Fig. 11 that lattices SEA is higher before densification happens. This can be explained by the fact that lattices samples are 5 times lighter than their composite counterparts. Average lattices SEA at densification is 1.00 J g -1 cm -3 . However, as the filling material is delaying densification, Hexaround composite lattices SEA at densification is finally 22% higher than simple ones, reaching 1.22 J g -1 cm -3 . Concerning absorption efficiency, Hexaround lattices reach an average 30.27% and composite lattices attain 52.73%. The increase efficiency can be explained by the delayed densification as well as the change of deformation behaviour: layerwise failure being less efficient than a plateau-like plasticity in this case.

Warmuth cell

In the case of the Warmuth cell, SEA of composite lattices are always higher than their simple lattice counterparts, being 60% higher at densification (see Fig. 11). Warmuth lattices reach an average SEA of 0.77 J g -1 cm -3 , and composite lattices an average 1.23 J g -1 cm -3 . Increased modulus and yield stress and especially delayed densification are responsible for increased SEA. The absorption efficiency of Warmuth lattices reaches an average 33.09% and composite lattices attain 48.31%. The increase efficiency occurs due to the delayed densification.

Crashworthiness properties of both lattices and composite lattices are reported in Table 6. One can conclude that filling auxetic lattices with compliant material increases SEA at densification, but has a less pronounced effect for intermediate strains. Specifically, the observed increase in SEA is linked to the ability of the composite lattices to delay densification. A consequent increase in absorption efficiency is observed for both unit-cells, stemming from different mechanisms : the Hexaround lattice is subjected to a different deformation behaviour from filling and both lattices benefit from delayed densification.

Discussion

In this work, we studied the effect of filling a compliant material into two auxetic structures. It was shown that composite lattices exhibit increased stiffness compared to their monolithic counterparts and the increase of the stiffness was varied depending on the lattice volume fraction. This observation is consistent with results reported in [START_REF] Novak | Mechanical properties of hybrid metamaterial with auxetic chiral cellular structure and silicon filler[END_REF] and [START_REF] Xue | Enhanced compressive mechanical properties of aluminum based auxetic lattice structures filled with polymers[END_REF]. However, in [START_REF] Xue | Enhanced compressive mechanical properties of aluminum based auxetic lattice structures filled with polymers[END_REF] the elastic modulus tends to increase from filling with high volume fraction lattices, even with high lattice volume fraction, which is in contradiction to our results. This can be explained by the high stiffness of the elastomers used, being 3300 to 6000 times stiffer than TB+, therefore providing a more efficient support. On the other hand, when the lattice structure is infiltrated with a harder polymer than used for the struts, a decreased or no change in specific Young's modulus has been reported in [START_REF] Li | Metallic microlattice and epoxy interpenetrating phase composites: Experimental and simulation studies on superior mechanical properties and their mechanisms[END_REF] and [START_REF] Osman | Compressive behavior of stretched and composite microlattice metamaterial for energy absorption applications[END_REF]. Evolution of composite lattices Young's modulus seems to be very dependent on the base material constitutive properties, specifically the modulus ratio between lattice and matrix 𝐸 lattice ∕𝐸 matrix .

When considering the Poisson's ratio our results indicate different trends to some earlier published work. For instance, Hexaround lattice minimal PR increases with volume fraction, until being completely non auxetic at high volume fraction. This trend is also followed by the composite Hexaround lattice structure where low volume fraction composite lattices show less auxeticity than simple lattices. Warmuth lattice minimal PR is less sensitive to the volume fraction evolution, but the maximal PR is higher for low volume fraction lattices. Composite Warmuth lattices exhibit lowest PR at high lattice volume fraction, where the matrix is having less influence on its behaviour. The presence of the soft phase tends to oppose auxetic deformation behaviour, making composite lattices less auxetic than simple ones. Increased PR from filling is also observed in [START_REF] Li | Exploiting negative Poisson's ratio to design 3d-printed composites with enhanced mechanical properties[END_REF][START_REF] Fíla | Impact testing of polymer-filled auxetics using split hopkinson pressure bar[END_REF] and [START_REF] Xue | Enhanced compressive mechanical properties of aluminum based auxetic lattice structures filled with polymers[END_REF], but no investigation on the effect of lattice volume fraction was made. In [START_REF] Zhang | Auxetic interpenetrating composites: A new approach to non-porous materials with a negative or zero Poisson's ratio[END_REF], composite auxetics exhibit a similar trend to Hexaround lattice where matrix increases the composite PR at low lattice volume fraction but its influence is decreasing with higher lattice volume fraction. As well as for normalized Young's modulus, effective Poisson's ratio of composite lattice depends on modulus ratio 𝐸 lattice ∕𝐸 matrix , as observed by [START_REF] Peng | Phase contrast mediated switch of auxetic mechanism in composites of infilled re-entrant honeycomb microstructures[END_REF]. While the present study only considered one pair of materials, further experiments could shed more light on the effect of different material properties ratio on the elastic properties of the composite lattice structures.

The compression tests revealed an important increase of stress level as well as peak stress resulting from filling with a soft phase. It showed that the composite stress level was not following a rule of mixture but demonstrated superior properties compared to its constituents. The stress resulting from the interaction between structure and matrix should be taken into account, as explained in [START_REF] Li | Metallic microlattice and epoxy interpenetrating phase composites: Experimental and simulation studies on superior mechanical properties and their mechanisms[END_REF]. Furthermore, it was observed that densification of lattices is postponed when filled with an elastomeric polymer. The opposite phenomenon has been observed on lattices filled with hard epoxy, in [START_REF] Li | Metallic microlattice and epoxy interpenetrating phase composites: Experimental and simulation studies on superior mechanical properties and their mechanisms[END_REF] and [START_REF] Osman | Compressive behavior of stretched and composite microlattice metamaterial for energy absorption applications[END_REF]. The delay in the densification was linked to a significant improvement in SEA and AE. In order to reveal mechanisms behind changes in deformation behaviour from filling further in-situ mechanical test using X-ray imaging should be conducted.

Conclusions and perspectives

In this work, mechanical properties of 2 different auxetic lattices filled with hyperelastic polymer are studied through both numerical and experimental approaches. Following conclusion can be drawn from this work:

1. Effective elastic properties (𝐸 * and 𝜈) of lattices and composites are compared using the numerical homogenization method, based on periodic boundary conditions. Five relative densities 𝑉 𝑓 of both Hexaround and Warmuth cell, obtained by varying struts diameter 𝐷, are compared. Results showed an increase of normalized Young's modulus due to filling, dependently on lattice initial modulus: the Hexaround see low change of modulus at high volume fraction, but important increase at low volume fraction. Warmuth cell being more compliant, its stiffness is highly increased at all lattice volume fraction. TangoBlack+ being nearly incompressible with a Poisson ratio close to 0.5, composite lattices Poisson's ratio is increased compared to simple lattices, with a strong influence of lattice volume fraction. Therefore, the lower the volume fraction of the lattice structure the larger the increase in its stiffness. 2. Lattices and composite lattices samples have been manufactured using Connex350 with VeroWhite and TangoBlack+ materials. Lattices were both manufactured at 20% volume fraction 𝑉 𝑓 .

Compression tests have been performed, showing that filling lattices with soft material induces an increase of Young's modulus (up to +316% for Warmuth cell, and +40% for Hexaround one), yield stress and peak stress, and delayed densification.

Finite element analysis shows good agreement with composite lattices experiments in the linear elastic part, but deviated in the plasticity region since the material behaviour did not account for damage. Good agreement between experiments and computational homogenization validated the selected strategy over full-field analysis. 3. During compression tests, the Hexaround lattice exhibits a layerwise failure mode, that is represented on stress/strain curves by five ''bumps'', corresponding to the five floors breaking one after the other. Hexaround composite lattices exhibit a completely different failure, involving shear band breaking. Warmuth lattice also shows a progressive failure, floor crumbling one after the other, but it cannot be clearly observed on stress/stress curves. Warmuth composite lattice exhibits structural buckling before a shear band breaking. 4. Comparison of Specific Energy Absorption and Absorption Efficiency 𝜂 is carried between manufactured lattices and composite lattices. The Warmuth composite cell exhibits superior SEA at all strain, up to 1.23 J g -1 cm -3 at densification, compared to simple lattice, which is not the case of the Hexaround that only displays superior SEA thanks to delayed densification, up to 1.22 J g -1 cm -3 . Both cells benefit of an increased absorption efficiency from filling, mainly because of delayed densification.

CRediT authorship contribution statement

Declaration of competing interest

No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/ 10.1016/j.addma.2021.102351.

Fig. 1 .

 1 Fig. 1. Hexaround (left) and Warmuth (right) unit-cells, with their periodicity vectors 𝑋 𝑖 (a), and geometric descriptions (b), and the strategy to create composite lattice structures (c).

  (a)): 𝐸 = 1.45 GPa; 𝜈 = 0.35; 𝜎 𝑌 = 20.0 MPa; 𝑄 1 = 19.3 MPa; 𝑏 1 = 137.7; 𝑄 2 = -39.6 MPa; 𝑏 2 = 10.1; 𝑄 3 = 51.5 MPa; 𝑏 3 = 4.3. VeroWhite's density is 1.175 g cm -3 .

  3(b)): 𝜇 = 0.155 MPa; 𝜆 = 2.87 MPa; d = 0.30. TangoBlack's density is 1.141 g cm -3 .

Fig. 2 .

 2 Fig. 2. Lattice samples of Hexaround and Warmuth structures after manufacturing (left side) shown in red and their composite counterparts filled with TangoBlack+ hyperelastic materials (right side).

Fig. 3 .

 3 Fig. 3. VeroWhite stress-strain curve and associated model (a); Tango-black+ stress-strain curve and associated model (b).

Fig. 4 .

 4 Fig. 4. Euler-Bunge angles.

Fig. 5 .

 5 Fig. 5. Representation of 𝑉 cubic and 𝑉 lattice .

Fig. 6 .

 6 Fig. 6. Hexaround (left) and Warmuth (right) elastic properties depending on loading orientation and lattice volume fraction.

Fig. 7 .

 7 Fig. 7. Influence of the filling soft phase on maximum normalized modulus (a)(c) and minimal Poisson's ratio (b)(d), for different lattice volume fraction.

Fig. 8 .

 8 Fig. 8. Change in the mode of failure from layerwise for the hexaround lattice (a) to shear band for the composite hexaround lattice (b).

Fig. 9 .Fig. 10 .

 910 Fig. 9. Von Mises equivalent stress maps within the truss for both simple (a) and composite (b) lattices at 3 levels of uniaxial compressive strain, resulting from FE simulations.

Fig. 11 .

 11 Fig. 11. SEA and Efficiency plot, Hexaround (left) and Warmuth (right).

Fig. A. 12 .

 12 Fig. A.12. Mesh sensitivity study for the Hexaround cell. 𝐸 ref being the converged normalized Young's modulus.

Fig. A. 13 .

 13 Fig. A.13. Mesh sensitivity study for the Warmuth cell. 𝐸 ref being the converged normalized Young's modulus.

Fig. B. 14 .

 14 Fig. B.14. 3D representation of the normalized directional elastic stiffness (Young's modulus as a function of orientation) for Hexaround and Warmuth cells at 0.05 and 0.25 volume fraction for both truss and composite lattices.

Fig. C. 15 .

 15 Fig. C.15. Stress/strain plot, Hexaround lattices and composite lattices compression test.

Fig. C. 16 .

 16 Fig. C.16. Sress/strain plot, Warmuth lattices and composite lattices compression test.

Frédéric Albertini :

 Albertini Investigation, Methodology, Software, Writing -original draft. Justin Dirrenberger: Conceptualization, Supervision, Methodology, Writing -review & editing. Cyrille Sollogoub: Supervision, Methodology, Writing -review & editing. Tobias Maconachie: Investigation, Writing -review & editing. Martin Leary: Writingreview & editing, Supervision. Andrey Molotnikov: Conceptualization, Supervision, Methodology, Writing -review & editing.

Table 1

 1 Hexaround cell geometrical parameters for different volume fraction.

	𝑉 𝑓 (-)	0.05	0.10	0.15	0.20	0.25
	𝐿 (mm)	6.0	6.0	6.0	6.0	6.0
	𝑎 (mm)	1.0	1.0	1.0	1.0	1.0
	𝐷 (mm)	0.39	0.56	0.70	0.83	0.94

Table 2

 2 Warmuth cell geometrical parameters for different volume fraction.

	𝑉 𝑓 (-)	0.05	0.10	0.15	0.20	0.25
	𝐿 (mm)	6.0	6.0	6.0	6.0	6.0
	𝑎 (mm)	1.0	1.0	1.0	1.0	1.0
	𝐷 (mm)	0.41	0.59	0.73	0.85	0.96

Table 3

 3 Theoretical (CAD) and average measured mass of manufactured samples.

	Sample	Mass:	CAD (g)	manufactured (g)
	Hexaround (lattice)		6.35	6.75 (± 0.11)
	Warmuth (lattice)		6.35	6.68 (± 0.13)
	Hexaround (composite lattice)	30.99	31.55 (± 0.09)
	Warmuth (composite lattice)	30.99	31.49 (± 0.10)

Table 4

 4 Identified Elastic properties of VeroWhite and TangoBlack+.

	Material	E (MPa)	𝜈 (-)
	VeroWhite	1450.0	0.35
	TangoBlack+	0.65	0.499

Table 5

 5 Comparison between lattices and composite lattices properties.

	Sample	Ēexp (MPa)	𝐸 hom (MPa)	𝐸 simul (MPa)	ξ𝑑 (-)	σpeak (MPa)
	Hexaround (lattice)	22.15 (± 1.3)	36.04	36.01	0.47 (± 0.04)	0.83 (± 0.05)
	Hexaround (composite)	31.04 (± 0.9)	42.24	39.13	0.65 (± 0.04)	2.63 (± 0.09)
	Warmuth (lattice)	3.75 (± 0.3)	11.08	10.96	0.49 (± 0.05)	0.58 (± 0.05)
	Warmuth (composite)	19.05 (± 1.1)	20.75	20.72	0.61 (± 0.07)	2.83 (± 0.10)

Table 6

 6 Experimentally recorded crashworthiness properties.

	Hexaround (lattice)	1.00 (± 0.05)	30.27 (± 2.1)
	Hexaround (composite)	1.22 (± 0.09)	52.73 (± 2.5)
	Warmuth (lattice)	0.77 (± 0.07)	33.09 (± 1.5)
	Warmuth (composite)	1.23 (± 0.11)	48.31 (± 5.2)

Sample

SEA 𝜉 = 𝜉 𝑑 (J.g -1 .cm -3 ) 𝜂 (%)

https://www.mcneel.com.

http://mumps.enseeiht.fr/.

Acknowledgements

F. Albertini and J. Dirrenberger acknowledge funding by the France-Australia Science Innovation Collaboration program as well as funding from Académie Francaise. Financial support from the French Department of Higher Education, Research and Innovation is gratefully acknowledged for funding F. Albertini's PhD scholarship. J. Dirrenberger acknowledge partial funding from the Agence Nationale de la Recherche, France through the ANR JCJC SCOLASTIC project (grant no. 16-CE08-0009). A. Molotnikov would like to acknowledge the financial support from the Rod Rickards Fellowship from the Australian Academy of Science.

Appendix A. Mesh convergence analysis

To ensure a mesh-independent response, a mesh convergence analysis has been performed, as shown in Figs. A.12 and A.13. Here, the number of elements in a mesh is considered sufficient if an error lower than 0.5% compared to a converged mesh is computed, the [100] relative elastic modulus being the object of the comparison.


Default OR or RAP (Ait Bout et al., 2021;Batlle et al., 2011;Brown et al., 2016;Carolan et al., 2011;Kautsky et al., 2016;Lavrentyeva et al., 2016;Robinson et al., 2010;Shishkina et al., 2016;Smith et al., 2010;Vandenhove et al., 2013, Stark et al., 2017) Species identified on site (Batlle et al., 2016;Charrasse et al., 2019;Jaeschke, B et al., 2013;Posiva, 2014;Torudd andSaetre, 2013, Stark et al., 2017) + 123,133,135,125,129,131 YES, in the vast majority of cases, by a factor of 2/3 Particular attention to short-lived RNs if they contribute mostly to the dose rate On the condition that the CRs/transfer factors used are identical between "real" and "reference" organism

The greatest uncertainty relies on the CR ratio (Johansen et al, 2012;Stark et al, 2015) Adding site specific species to the set of reference organism can respond to various interests, such as demonstrating to the stakeholders more specifically the actual protection of the environment

2008 

 2008 of biological diversity, the conservation of species, or the health and status of natural habitats, communities, and ecosystems" … Objectives of the ICRP / IAEA "It also recognised the needs of some national authorities to demonstrate, directly and explicitly, that the environment is being protected…" AND 2018 System developed in coherence with that for humans The approaches are based on a set of reference

**

  the use of the generic organisms defined by different approaches in a risk assessment really protect all species in the different target ecosystems in terms of dosimetry?" ? MODARIA II program from the IAEA (Modelling and Data for Radiological Impact Assessments) Collaboration with the WG 3 (« Assessments and control of exposures to public and biota for planned releases to the environment »)ICRP, 2008; 2009; WTD; www. wildlifetransferdatabase.org/, Copplestone et al., 2013, Beresford et al, 2016 Assumptions for endangered/protected species or not well characterized species :ICRP, 2008; 2009; WTD; www. wildlifetransferdatabase.org/, Copplestone et al., 2013, Beresford et al, 2016

CONCLUSION"

  Pragmatic question : Does the use of the generic organisms defined by different approaches in a risk assessment really protect all species in the different target ecosystems in terms of dosimetry?"

French Alternative Energies and Atomic Energy Commission 8

Activity concentration in the media

The question comes down to

What is the influence of the diversity of sizes and shapes of the ellipsoid + Habitat diversity ? Intra-DR tot difference less than a factor of 2

Despite the range of geometric characteristics, habits and habitats numerical risk assessment is not improved for any selected biota in this release scenario 14

DE LA RECHERCHE À L'INDUSTRIE

French Alternative Energies and Atomic Energy Commission -www.cea.fr

THANKS FOR YOUR ATTENTION 

A special thanks to all the participants from the WG3 and the scientific secretaries


Qingfeng Shao

Jean-Jacques Bahain

Christophe Falgueres

Carlo Peretto

Marta Arzarello

Antonella Minelli

Ursula Thun Hohenstein

Jean-Michel Dolo

Tristan Garcia

Norbert Frank

Christophe Falguères

Eric Douville

New ESR/U-series data

Keywords: Isernia la Pineta, ESR/U-series dating, Tooth enamel, Gamma dose rate, Early Middle Pleistocene

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

Introduction

Isernia la Pineta, unexpectedly discovered in 1978 near Rome, Italy, (Fig. 1A) is one of the most important Early Palaeolithic sites in Europe [START_REF] Balter | In search of the first Europeans[END_REF]. Numerous fauna remains and Oldowan-like artefacts (Mode I) have been found there within a thick stratigraphy made up of fluvial, lacustrine and volcanic sediments [START_REF] Coltorti | Reversed magnetic polarity at an early Lower Palaeolithic site in Central Italy[END_REF][START_REF] Peretto | Isernia la Pineta, un accampamento piu antico di[END_REF]) (Fig. 1B). The geological age of this site has been evaluated by various dating methods, such as 40 K/ 40 Ar [START_REF] Coltorti | Reversed magnetic polarity at an early Lower Palaeolithic site in Central Italy[END_REF][START_REF] Sevink | A note on an approximately 730 000 year old mammal fauna and associated human activity sites near Isernia, Central Italy[END_REF], palaeomagnetism [START_REF] Coltorti | Reversed magnetic polarity at an early Lower Palaeolithic site in Central Italy[END_REF][START_REF] Gagnepain | Etude magnétostratigraphique de sites du Plésitocène inférieur et moyen des Alpes-Maritimes et d'Italie: Grotte du Vallonnet, Marina Airport, Ca' Belvedere di Monte Poggiolo[END_REF] and biostratigraphy [START_REF] Peretto | Isernia la Pineta, un accampamento piu antico di[END_REF][START_REF] Peretto | I reperti paleontologici del giacimento paleolitico di Isernia La Pineta: l'uomo e l'ambiente, Istituto Regionale per gli Studi Storici del Molise[END_REF], and strongly debated according to the palaeontological record [START_REF] Roebroeks | The earliest occupation of Europe: a short chronology[END_REF]Van Kolfschoten, 1994, Von Koenigswald and[START_REF] Von Koenigswald | The Mimomys-Arvicola boundary and the enamel thickness quotient (SDQ) of Arvicola as stratigraphic markers in the Middle Pleistocene[END_REF]. The normal magnetization recorded on the whole sequence [START_REF] Gagnepain | Etude magnétostratigraphique de sites du Plésitocène inférieur et moyen des Alpes-Maritimes et d'Italie: Grotte du Vallonnet, Marina Airport, Ca' Belvedere di Monte Poggiolo[END_REF] and the date of 610 ± 10 (2σ) ka, obtained by 39 Ar/ 40 Ar dating on sanidines from the geological level (U3E), located immediately above the archeological layer, t3a [START_REF] Coltorti | New 40 Ar/ 39 Ar, stratigraphic and palaeoclimatic data on the Isernia la Pineta Lower Palaeolithic site[END_REF] put the Isernia assemblage in the early part of Middle Pleistocene. It is in good agreement with palaeontological features, such as the presence of the rodent Arvicola cantiana and its association with Bison schoetensacki, Stephanorhinus hundsameinsis and Elephas antiquus.

From the biostratigraphical point of view, Isernia la Pineta can be correlated with the palaeoanthropological Mauer site, Germany recently dated to around 600 ka by infrared radiofluorescence and ESR/U-series methods [START_REF] Wagner | Radiometric dating of the type-site for Homo heidelbergensis at Mauer, Germany[END_REF].

Combined ESR/U-series method on tooth enamel [START_REF] Grün | ESR dating of tooth enamel: coupled correction for Uuptake and U-series disequilibrium[END_REF] is frequently applied to date palaeontological and archeological sites and it was demonstrated that this method can potentially cover all the Middle Pleistocene period [START_REF] Falguères | Earliest humans in Europe: the age of TD6 Gran Dolina, Atapuerca, Spain[END_REF]. However, at Isernia, two previous ESR/U-series dating studies failed. Hence, [START_REF] Bahain | ESR dating of tooth enamel: a comparison with K-Ar dating[END_REF] studied five teeth of different mammal species (bovid, rhinoceros and elephant) and obtained severely underestimated ages ranging between 80 and 250 ka. As explanation, they attributed the underestimated ages to an inhomogeneous U distribution through the enamel and to the presence of short-life components in tooth enamel ESR spectra [START_REF] Bahain | ESR dating of tooth enamel: a comparison with K-Ar dating[END_REF].

More recently, [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF] reported new ESR/U-series dates of 560 ± 84 ka for one bovid and of 345 ± 67 ka (weighted mean age) for five rhinoceros teeth. In this study, the ESR/U-series ages were calculated using a mean value for the external γ-dose rate (1650 μGy/a) evaluated by six thermoluminescence (TL) dosimeters positioned near the studied teeth. Considering the numerous palaeontological remains deposited in the archeological layer and the recent U-uptake demonstrated for 9/14 of the dental tissues, the authors postulated that the external γ-dose rate, which represents 44-73% of the total dose rate when integrated with respect to time, caused the incompatibility between these ESR/U-series dates and 39 Ar/ 40 Ar age. The difference of ESR/U-series ages between the two analyzed mammal species was seen as the result of 'taxonomic' effect and the analysis of additional bovid teeth was decided to clarify this point [START_REF] Bahain | La méthode de datation par résonance de spin électronique (ESR) au Muséum national d'histoire naturelle -Vingt ans de recherches méthodologiques et d'applications géochronologiques[END_REF].

The present paper shows the ESR/U-series dating results obtained from new analyses of bovid teeth (B. schoetensacki) and proposes a dose rate reconstruction hypothesis, to simulate γ-dose change at Isernia and to evaluate the impact of such change on the age calculation, considering the 39 Ar/ 40 Ar age of 610 ± 10 ka as the reference.

Materials and methods

Four bovid teeth, collected from the archeological layer t3a, were used in the present study (Fig. 1C). In situ γ-dose rate was measured using two independent methods: portable γspectrometry [START_REF] Mercier | Field gamma dose-rate measurement with a NaI(TI) detector: reevaluation of the "threshold" technique[END_REF] and TL CaSO4:Dy dosimeters [START_REF] Valladas | Mesure de la dose gamma annuelle de l'environnement d'un site archéologique par un dosimètre TL[END_REF]. Additional γ-spectroscopy measurements were performed in the laboratory to determine the external β-dose rate for sediment samples collected from within 5 cm of the teeth.

The dental tissues (enamel, dentine, and cement) of each tooth were separated and cleaned mechanically using a dentist's drill. Enamel was manually crushed, then sieved. Nine enamel aliquots (about 100 mg each) of the 100-200 μm grain-size fraction were irradiated following an exponential dose distribution [START_REF] Grün | Simulations of saturating exponential ESR/TL dose response curvesweighting of intensity values by inverse variance[END_REF]) at 500, 800, 1250, 2000, 3200, 5000, 8000, 12 500 and 20 000 Gy using a calibrated 60 Co γ-ray irradiator (LNHB, CEA). ESR-signal intensities of irradiated and natural aliquots were measured ten times by EMX Bruker X-band spectrometer. The equivalent doses, DE, were determined from the asymmetric enamel signal by the additive method, using a single saturated exponential function following [START_REF] Yokoyama | ESR dating of quartz from Quaternary sediments: first attempt[END_REF].

We carried out U-series analyses for each dental tissue with Inductively Coupled Plasma-Quadrupole Mass Spectrometry (ICP-QMS) [START_REF] Douville | Rapid and accurate U-Th dating of ancient carbonates using inductively coupled plasma-quadrupole mass spectrometry[END_REF]. The used chemical protocol was: 50-150 mg of each sample was dissolved in 7 N HNO3 and spiked with 233 U, 236 U and 229 Th. The solution was loaded onto an anion exchange resin column (Dowex 1 × 8; 100-200 mesh) in 8 N HCl. In such condition, Th passed the column straight through and U was fixed. Then it was eluted with 0.1 N HCl. U and Th fractions were purified using respectively a UTEVA resin column in 7 N HNO3 and a second anion exchange resin column in 7 N HNO3. In such strong acid conditions, U and Th were retained on resin columns. They were then eluted with 0.1 N HCl for U and 8 N HCl for Th. The purified U and Th isolates were then evaporated and residues were dissolved in 0.5 N HNO3 and recombined before the ICP-QMS analyses. ICP-QMS is an optimized time-consuming technique for U-series isotopic analysis given uncertainties of about 0.4% and 1% for U and Th isotopes respectively [START_REF] Douville | Rapid and accurate U-Th dating of ancient carbonates using inductively coupled plasma-quadrupole mass spectrometry[END_REF]. The analytical uncertainties associated to U-series ages were here about few percents (3-10%) at 2σ level (Table 1). ESR/U-series ages were calculated using "DATA" [START_REF] Grün | The DATA program for the calculation of ESR age estimates on tooth enamel[END_REF] with the dose rate conversion factors reported by Adamiec and Aitken (1998) and using the following parameters: a k-value of 0.13 ± 0.02 (Grün and Katzenberger-Apel, 1994); a water content of 3 wt% in the enamel [START_REF] Driessens | The mineral in bone, dentine and tooth enamel[END_REF], 10 wt% in dentine and in cement, and 20 wt% in sediment; β-attenuations in the enamel layers following [START_REF] Brennan | B-doses in tooth enamel by 'One Group' theory and the Rosy ESR dating software[END_REF]; cosmic dose rate by the formula of [START_REF] Prescott | Cosmic ray contributions to dose rates for luminescence and ESR dating: large depths and long-term time variations[END_REF] and taking into account the overlying sediment thickness evolution. The effect of radon loss in each tissue was determined by combining α-ray and γ-ray data [START_REF] Bahain | ESR dating of tooth enamel: a comparison with K-Ar dating[END_REF].

Sample

Results and discussion

Table 1 shows the results of U-series analyses. U contents range from 2.6 to 4.4 ppm in enamel, and from 120 to 237 ppm in dentine and cement. 234 U/ 238 U and 230 Th/ 234 U activity ratios range respectively between 1.25 and 1.37, and between 0.54 and 0.91, which allow the determination of the apparent 230 Th/ 234 U ages ranging from 82 to 205 ka, confirming the previously mentioned recent U-uptake into the Isernia samples. The four new teeth, as the six reported previously [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF], were recovered from the same archeological surface. They show very similar U-series data indicating that this layer seems to have relatively homogenous U-series geochemical processes. Concerning the equivalent doses, the new obtained data agree with the DE from one of the five rhinoceros teeth dated previously (IS9906, 1637 ± 215 Gy) and from the bovid tooth (IS9902, 1809 ± 103 Gy). They are substantially greater than that for the other four rhinoceros teeth (ranging from 787 ± 55 to 1065 ± 53 Gy) [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF]. By comparison, we observed that, on the one hand, the bovid teeth generally show higher equivalent doses than that of rhinoceros. On the other hand, the equivalent dose varies apparently by a factor of 1.5 for the five bovid teeth, and by a factor of 2.1 for the five rhinoceros teeth. If the 200 ka dating gap is due to the DE determination, DE would be underestimated by about 22% for IS0901, 41% for IS0902, 18% for IS0903 and 27% for IS0904. However, in this work, ESR intensities were ten times measured on the range of time ranging between 4 and 12 months after irradiation, without any significant variation of the DE values. DE errors were estimated lower than 15% (2σ), and we thus can confidently exclude blaming the age underestimations on DE determinations.

Variation in the external γ-dose rate was suggested by [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF] to explain the age underestimation, in relation with U-uptake histories of the numerous palaeontological remains of t3a level. In this previous study, the mean γ-dose rate value (1650 μGy/a) used for the age calculation was evaluated by 6 TL dosimeters and represented 44-73% of total dose rate [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF]. Our new in situ measurements using a γ-ray spectrometer confirm this high γ-dose rate in the t3a archaeological layer (Table 2 and Fig. 1).

The work by [START_REF] Blackwell | Considering sedimentary U uptake in external dose rate determinations for ESR and luminescent dating[END_REF] suggested that in situ γ or TL dosimetry tends to overestimate the time-averaged dose rates in the sediments containing numerous bone and tooth fragments that absorb U. Indeed, this phenomenon is emphasized at Isernia, because the palaeontological remains show both high uranium concentrations and recent U-uptakes, revealed by young apparent 230 Th/ 234 U ages and mostly positive p-values (Table 1, Table 2). As the t3a layer, around 30 cm thick, displays high fossil density (Fig. 1C andD), both the sediments and above all these fossils contribute to the γ-dose rate. During the burial history, if the fossils have experienced similar recent U-uptake processes as the analyzed dental tissues, the external γ-dose rate would have increased since the archaeological event we want to date.

Then the present-day measured γ-dose rates should be considered as maximum values throughout burial history, but not as the geological values required for the age calculations.

According to their U-series results, [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF] suspected that a drastic change of the γ-dose rate in the layer of Isernia t3a occurred perhaps during MIS 5. The deepening of the Volturno Valley near Isernia is considered as younger than the top of the archeological stratigraphy [START_REF] Cremaschi | La serie pleistocenica di Isernia la pineta (Molise) e la posizione stratigraphica dei suoli d'abitato paleolitici in essa inclusi[END_REF][START_REF] Coltorti | New 40 Ar/ 39 Ar, stratigraphic and palaeoclimatic data on the Isernia la Pineta Lower Palaeolithic site[END_REF] and the associated evolution of ground water circulation could be at the origin of this dosimetric change. In a simplistic way, we assume that this change is related to a unique event, which probably occurred during a wet interglacial period younger than 474 ± 6 ka [START_REF] Coltorti | New 40 Ar/ 39 Ar, stratigraphic and palaeoclimatic data on the Isernia la Pineta Lower Palaeolithic site[END_REF]. So we simulated that the variation of γdose rate occurred during MIS 11, 9, 7 or 5. The mean γ-dose rate value of 850 μGy/a determined by TL dosimeters in the sediments underlying t3a layer in the same geological unit (Unit U3F, Fig. 1B) [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF], was used as the dose rate before the massive Uuptake event, then the present-day values were used subsequently to this event.

The simulated dose rates and correlative ESR/U-series ages are listed in Table 3. We can observe a gradually decrease of the γ + cosmic contributions for dose rates and a simultaneous increase of the ESR/U-series ages (Table 3 and Fig. 2). For example, for IS0901 tooth, the contribution of the γ + cosmic dose rate to total annual dose decreases from 53% using in situ value to 52%, 50%, 48% and 46%, if the change event occurred during MIS 11, 9, 7, or 5, respectively. Consequently, IS0901 age increases from 456 ± 54 ka to 492 ± 99, 556 ± 108, 630 ± 115 and 734 ± 123 ka, respectively. [START_REF] Lisiecki | A Pliocene-Pleistocene stack of 57 globally distributed benthic δ 18 O records[END_REF]. The "In-situ, MIS 11, MIS 9, MIS 7 and MIS 5" ages are the weighted mean (W = 1/σ 2 ) ESR/U-series dates calculated using the present-day dosimetry value and the simulated γ-dose rates for the different MIS respectively. The ESR/U-series ages are given with ±1σ while 39 Ar/ 40 Ar one [START_REF] Coltorti | New 40 Ar/ 39 Ar, stratigraphic and palaeoclimatic data on the Isernia la Pineta Lower Palaeolithic site[END_REF] is given with ±2σ.

Altogether, the γ + cosmic dose rate contribution represents 52-64% of the total dose rates if we consider that the main U-uptake is associated to MIS 11 against 46-56% if this event is simulated during MIS 5. The error weighted mean ESR/U-series ages increase from 457 ± 45 ka in the MIS 11 scenario to 706 ± 55 ka in the MIS 5 one (Fig. 2). The comparison of these results with the 39 Ar/ 40 Ar date suggests that the change of γ-dose rate could be occurred during MIS 7 (about 240 ka), if we consider the mean ESR/U-series age (601 ± 51 ka) (Fig. 2). This simplistic simulation indicates that such a geological change impacts greatly on the ESR/U-series ages in case of recent U-uptake behaviour of the palaeontological remains.

Conclusions

Isernia la Pineta is one of the main European archeological and palaeontological sites for the Early Palaeolithic period, dated to 610 ± 10 ka by 39 Ar/ 40 Ar. Although ESR/U-series dating method on tooth enamel has been successfully applied to many sites, previous studies performed on Isernia samples failed. In the present work, the routine use of the ESR/U-series method on bovid teeth provided once again underestimated results with error weighted mean age of 435 ± 24 ka, approximately 200 ka younger than the 39 Ar/ 40 Ar date.

For the Isernia samples, we suggest that such underestimation may be linked to a change of the γ-dose rate during the geological times in relation with a recent U-uptake into the palaeontological remains. The 30 cm thick t3a archeological layer contains an exceptional accumulation of large mammal bones which have incorporated uranium posterior to their burial, with drastic consequences on the post-depositional change about the γ-dose rate. Thus the present-day in situ γ-dose rate should be regarded as a maximum value over the whole burial history.

To determine ESR/U-series age for the Isernia samples, time-integrated γ-dose rate should be reconstructed. A two steps γ-dose rate evolution based on our assumption of a correlation between a massive U-uptake event and a past wet interglacial period (MIS 11, 9, 7 or 5) was created to simulate the variations of the γ-dose rate. The results indicates, if the 39 Ar/ 40 Ar date is used as reference, that the assumed change event most likely occurred during MIS 7, rather than during MIS 5 as previously suggested by [START_REF] Falguères | On the interest and the limits of using combined ESR/U-series model in the case of very late uranium uptake[END_REF]. The use of this mathematical model can hence help to evaluate the effects of γ-dose rate variations on age calculations, but it requires independent age constraints. Therefore geological dosimetric change could limit the application of ESR/U-series dating method to the sites with numerous palaeontological remains displaying recent U-uptake evidence.

Fig. 1 .

 1 Fig. 1. Isernia la Pineta Middle Pleistocene site, Italy. A -Location; B -Stratigraphy; C -Partial map of the t3a archaeological layer (by courtesy of Giuseppe Lembo) with original location of the analyzed samples and dosimetry points; D -Picture of the t3a archaeological layer (the photographed area is located on the map by a dotted square). The two elephant bones, around 2 m long, on each side of the picture, give the scale.

Figure 2 .

 2 Figure 2. Comparison of combined ESR/U-series dates with 39 Ar/ 40 Ar age of Isernia Palaeolithic site (with isotopic data from[START_REF] Lisiecki | A Pliocene-Pleistocene stack of 57 globally distributed benthic δ 18 O records[END_REF]. The "In-situ, MIS 11, MIS 9, MIS 7 and MIS 5" ages are the weighted mean (W = 1/σ 2 ) ESR/U-series dates calculated using the present-day dosimetry value and the simulated γ-dose rates for the different MIS respectively. The ESR/U-series ages are given with ±1σ while 39 Ar/ 40 Ar one[START_REF] Coltorti | New 40 Ar/ 39 Ar, stratigraphic and palaeoclimatic data on the Isernia la Pineta Lower Palaeolithic site[END_REF] is given with ±2σ.

Table 1 .

 1 U-series data (±2σ) obtained by ICP-QMS on Isernia bovid teeth.

						Apparent
		Tissue	U (ppm)	234 U/ 238 U	230 Th/ 234 U	230 Th/ 234 U
						age (ka)
	IS0901	Enamel	3.776 ± 0.015	1.355 ± 0.001 0.673 ± 0.023 114 ± 9
		Dentine	225.201 ± 1.073 1.314 ± 0.005 0.720 ± 0.008 129 ± 3
		Cement	120.331 ± 0.768 1.327 ± 0.009 0.770 ± 0.018 146 ± 9
	IS0902	Enamel	3.249 ± 0.011	1.343 ± 0.001 0.691 ± 0.031 120 ± 12
		Dentine	193.608 ± 0.952 1.276 ± 0.005 0.695 ± 0.010 122 ± 4
	IS0903	Enamel	4.387 ± 0.008	1.320 ± 0.001 0.543 ± 0.016 82 ± 4
		Dentine	237.290 ± 1.069 1.263 ± 0.005 0.574 ± 0.009 90 ± 3
		Cement	216.027 ± 1.044 1.253 ± 0.010 0.621 ± 0.014 102 ± 5
	IS0904	Enamel	2.616 ± 0.008	1.343 ± 0.001 0.683 ± 0.037 118 ± 14
		Dentine	201.837 ± 1.144 1.276 ± 0.005 0.686 ± 0.009 119 ± 4
		Cement	126.928 ± 0.967 1.362 ± 0.013 0.901 ± 0.015 205 ± 13

Table 2

 2 summarizes the results of ESR/U-series dating of these bovid teeth. The equivalent doses, DE, range from 1238 ± 61 to 1645 ± 113 Gy and the combined ESR/U-series ages from 400 ± 42 to 471 ± 59 ka, with an error weighted mean age of 435 ± 24 (1σ) ka. These dates are consistent with the previous ESR/U-series results, but are not compatible with the 39 Ar/ 40 Ar date. They indicate that either DE was systematically underestimated or dose rate was overestimated.

	Samp le	DE (Gy)	Intern al	Dose rate (μGy/a) β γ + cos mic	Total	Enamel	p-parameter Dentine	Cement	ESR/ US age (ka)
	IS0901	1645 ± 1 13	448 ± 3 7	1264 ± 76	1910 ± 50	3622 ± 99	0.743 ± 0.2 56	0.385 ± 0.2 10	0.071 ± 0.16 7	456 ± 5 4
	IS0902	1238 ± 6 1	401 ± 2 8	713 ± 4 3	1990 ± 50	3104 ± 71	0.362 ± 0.1 87	0.323 ± 0.1 84		400 ± 4 2
	IS0903	1360 ± 8 8	284 ± 3 0	888 ± 6 6	1720 ± 50	2892 ± 88	2.2 ± 0.466	1.796 ± 0.4 13	1.275 ± 0.34 3	471 ± 5 9
	IS0904	1455 ± 8 9	321 ± 2 3	1043 ± 42	1945 ± 50	3309 ± 69	0.599 ± 0.2 09	0.563 ± 0.2 06	-0.551 ± 0. 072	441 ± 4 6

Table 2 .

 2 Combined ESR/U-series data obtained on Isernia bovid teeth. Uncertainties are given with ±1σ.

Table 3 .

 3 Effect of the modelled gamma dose changes on the ESR/U-series data obtained on Isernia bovid teeth. Uncertainties are given with ±1σ.

	Mome nt of the chang e of etry dosim	Sam ple	Simulated dose rate (μGy/a) Inter nal β γ + cos mic Total	Enamel	p-parameter Dentine	Cement	Simul ated (ka) ESR/ US age	Error weigh (ka) ted mean age
	MIS 5	IS09	316 ±	908 ±	1031 ±	2255 ±	2.012 ±	1.411 ±	0.874 ± 0.	734 ±	706 ±
	(125 k	01	41	81	50	104	0.538	0.429	328	123	55
	a)	IS09	287 ±	561 ±	1070 ±	1918 ±	1.427 ±	1.367 ±		649 ±
		02	33	47	50	76	0.421	0.413		100
		IS09	187 ±	584 ±	991 ±	1762 ±	4.558 ±	3.880 ±	2.997 ± 0.	774 ±
		03	26	58	50	81	0.953	0.840	691	124
		IS09	232 ±	816 ±	1046 ±	2094 ±	1.734 ±	1.682 ±	-0.209 ±	699 ±
		04	26	47	50	73	0.440	0.434	0.120	102
	MIS 7	IS09	355 ±	1012 ±	1254 ±	2621 ±	1.550 ±	1.040 ±	0.588 ± 0.	630 ±	601 ±
	(240 k	01	49	98	50	121	0.519	0.418	326	115	51
	a)	IS09	327 ±	613 ±	1355 ±	2295 ±	0.970 ±	0.919 ±		542 ±
		02	39	56	50	84	0.389	0.381		90
		IS09	212 ±	658 ±	1161 ±	2031 ±	3.770 ±	3.184 ±	2.424 ± 0.	672 ±
		03	34	75	50	96	0.947	0.836	690	122

Acknowledgements

This study was realized with the financial support of the ATM "Relations homme-nature sur le long terme" of the Muséum National d'Histoire Naturelle. The authors thank the excavation team of Isernia la Pineta for the help and welcome on the field (with special thanks to Annarosa Di Nucci and Giuseppe Lembo who provided respectively the analyzed teeth and the map of the archaeological t3a layer) and Farida Selmet and Yamna Badday for their help during the preparation of the mission. ICP-QMS analyses were performed at the Laboratoire des Sciences du Climat et de l'Environnement (LSCE/IPSL, UMR8212 CNRS-CEA-UVSQ), Gif sur Yvette, France. The ESR spectrometer of the French National Museum of Natural History was bought with the financial support of the 'Sesame Île-de-France' programme.