Benjamin Vaissier
email: benjamin.vaissier@ensam.eu

Jean-Philippe Pernot
email: jean-philippe.pernot@ensam.eu

Laurent Chougrani

Philippe Véron

Parametric design of graded truss lattice structures for enhanced thermal dissipation ✩,✩✩

Keywords:

Truss lattice structures are intricate geometries, whose fabrication has recently been simplified by the development of Additive Manufacturing (AM) technologies. These lightweight geometries present great volume densities and surface-to-occupancy ratios, which makes them ideal for thermal dissipation applications. This paper introduces a new framework for the parametric design of graded truss lattice structures that maximize passive cooling. It exploits the results of a semi-analytic formulation and analysis of the volume density and surface-to-occupancy ratio of state-of-the-art unit cells. In particular, it comes out that any truss lattice structure presents an optimal beam diameter over unit cell size ratio that maximizes its surface-to-occupancy value. This value and the ratio for which it is reached are identified and compared for the most common unit cells. The unit cell with the maximal surface-to-occupancy ratio is then identified, along with its set of optimal parameters, taking into account additive manufacturing constraints. The validation of this optimal geometry is performed by populating pre-defined design spaces of both academic and industrial case studies. An orientation strategy and a parametric gradation approach are also proposed to further optimize the generated heat sinks and maximize passive cooling. These results are very helpful to support decision making during the parametric design of a heat sink and to identify, a priori, the optimal unit cell, its control parameters, its orientation and its gradation strategy. The generated geometries are compared with traditional heat sink structures through static heat dissipation simulations, in order to demonstrate their interest.

Introduction

Recently developed Additive Manufacturing (AM) technologies are experiencing a great popularity rise among manufacturing companies, enabling the fabrication of intricate parts so far inconceivable [START_REF] Gao | The status, challenges, and future of additive manufacturing in engineering[END_REF]. Indeed, these breakthrough technologies catch the attention of many industrial fields (e.g. aerospace, automotive, defense or medical sectors) very much interested in exploring the design capabilities of AM to create high-value metallic or plastic components [START_REF] Tofail | Additive manufacturing: scientific and technological challenges, market uptake and opportunities[END_REF]. As opposed to subtractive manufacturing technologies, AM consists in joining materials to create objects framework to support the design and generation of such intricate geometries. These lightweight geometries present great volume densities and surface-to-occupancy ratios, and are therefore very well suited for the design and optimization of heat sinks. Fig. 1 shows heat sinks designed by means of traditional fins or incorporating a graded lattice structure following the framework proposed in this paper. However, these ratios may vary depending on the adopted type of unit cell, its intrinsic parameters, its orientation and gradation within the lattice structure, all of which are being studied in this paper. More precisely, this article demonstrates that any truss lattice structure presents an optimal beam diameter over unit cell size ratio that maximizes its surface-to-occupancy value. This value and the ratio for which it is reached are identified and compared for the most common state-of-the-art truss lattices. The unit cell with the maximal surface-to-occupancy ratio is then identified, along with its set of optimal parameters, taking into account additive manufacturing constraints. The validation of this optimal geometry is performed by populating pre-defined design spaces of both academic and industrial case studies. An orientation strategy and a parametric gradation approach are also proposed to further optimize the generated heat sinks and maximize passive cooling. These results are very helpful to support decision making during the parametric design of a heat sink and to identify, a priori, an optimal unit cell, its control parameters, its orientation and gradation strategy. The generated geometries are compared with traditional heat sink structures through static heat dissipation simulations.

The contribution is threefold: (i) a new framework for the parametric design of graded truss lattice structures that maximize passive cooling, (ii) a semi-analytic formulation and a theoretical analysis of the volume densities and surface-to-occupancy ratios for state-of-the-art unit cells, in order to support decision making and identify a priori the optimal unit cell and its control parameters, (iii) an approach to generate printable well-oriented and graded truss lattice structures, in order to further enhance the dissipation performances.

The paper is organized as follows. After an overview of the current developments on thermal dissipation geometries (Section 2), Section 3 describes the overall framework composed of several steps. The semi-analytic formulation and the theoretical analysis of the volume densities and surface-to-occupancy ratios of the most common unit cells are detailed in Section 4. In Section 5, the approach is then discussed and validated on both academic and industrial case studies, and the performances are compared with the ones obtained by other heat sinks designs. Section 6 ends this paper with conclusions and perspectives.

Related works

To cool down a system generating thermal energy, one of the classical ways is to surround the hot temperature source by a heat sink, in order to maximize the thermal exchange area between the source and its environment [START_REF] Ahmed | Optimization of thermal design of heat sinks: A review[END_REF]. This simple refrigeration mechanism is called static heat conduction or passive cooling, and this is the type of thermal dissipation considered in this article. Actually, due to their robustness and low maintenance requirements, those self-contained passive cooling technologies are much used in many industrial systems. To increase the cooling performances, an additional solution consists in creating a heat conducting fluid flow (e.g. air, water or cooling liquid) around the heat sink in order to avoid thermal accumulation at its surface. This approach is called forced heat convection or active cooling. It is not directly considered here, even though some of the results of this article could be exploited to extend the proposed approach for this type of dissipation. This is further discussed in the conclusion.

Because thermal energy dissipation problems are governed by partial differential equations derived from the first law of thermodynamics, the optimal heat sink geometry is generally extremely hard to find analytically when considering real-life configurations [START_REF] Kraus | Extended surface heat transfer[END_REF]. This is why, over the years, various generic geometries, from the simplest to the most intricate one, have been explored and tuned to resolve this kind of problems [START_REF] Jafari | The utilization of selective laser melting technology on heat transfer devices for thermal energy conversion applications: A review[END_REF]. The pros and cons of the available solutions are discussed in the next paragraphs.

Fins and pins: these simple geometries are often generated by extruding a constant cross-section in a rectilinear direction. Fins consist of thin walls regularly spaced out, whereas pins are vertical pillars distributed over the heating surface. The classical rectangular cross-section of fins can be morphed into spine shapes, in order to increase thermal dissipation efficiency [START_REF] Kraus | Extended surface heat transfer[END_REF][START_REF] Pirompugd | Efficiencies for partially wetted spine fins: Uniform cross section, conical, concave parabolic, and convex parabolic spines[END_REF]. Likewise, the heat transfer rate of pins with a circular cross-section can be increased by shaping them like airfoils, reducing the turbulence in the convective air flow [START_REF] Ho | Convective heat transfer performance of airfoil heat sinks fabricated by selective laser melting[END_REF]. Fractal-like pins microstructures have also been explored for the design of optimized heat sink geometries [START_REF] Massarwi | Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition[END_REF]. However, fins and pins, which are among the simplest heat sinks geometries, do not present optimal surface-to-occupancy ratios which limits their performance.

Open-cell foams: these lightweight metamaterials can be defined as porous materials with interconnected cavities. Open-cell foams present good surface-to-occupancy ratios, which make them good candidates for thermal dissipation [START_REF] Ashby | Metal Foams: A Design Guide 263[END_REF][START_REF] Mahjoob | A synthesis of fluid and thermal transport models for metal foam heat exchangers[END_REF]. Experimental studies have been carried out on metal foams in order to have a better understanding of their geometrical [START_REF] Nie | Modeling structures of open cell foams[END_REF], mechanical [START_REF] Murr | Characterization of ti-6al-4v open cellular foams fabricated by additive manufacturing using electron beam melting[END_REF] and thermal [START_REF] Wu | Thermal conductivity model of open-cell foam suitable for wide span of porosities[END_REF] characteristics. However, because of their random nature, these properties are hard to model or simulate. This makes them unsuited for a priori parametric design, especially in the case of heat sink design [START_REF] Feng | An experimental and numerical study of finned metal foam heat sinks under impinging air jet cooling[END_REF].

Surface-based lattices: defined by the thickening of Triply-Periodic Minimal Surfaces (TPMS), which are mathematical 3D functions with zero mean curvature everywhere (locally minimizing their area), surface-based lattice structures are used in particular by the medical industry to generate implants with enhanced osseointegration properties [START_REF] Mahmoud | Lattice structures and functionally graded materials applications in additive manufacturing of orthopedic implants: A review[END_REF]. Indeed, like open-cell foams, they demonstrate good surface-to-occupancy ratios, and the exact formulas for these ratios have long been known [START_REF] Gandy | Exact computation of the triply periodic d 'diamond'/ minimal surface[END_REF]. Parametric optimization has even been considered to minimize the surface area of various TPMS [START_REF] Yang | A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint[END_REF]. However, despite many investigations on their mechanical properties [START_REF] Li | Optimal design and modeling of gyroid-based functionally graded cellular structures for additive manufacturing[END_REF], very few works are focusing on TPMS thermal applications [START_REF] Abueidda | Effective conductivities and elastic moduli of novel foams with triply periodic minimal surfaces[END_REF].

Truss lattices: defined as the aggregation of interconnected beams, truss (or beam-based) lattices can be classified into 2 subgroups: triply periodic lattices (TPL), and stochastic lattices (SL). Both present good surface-to-occupancy ratios, which makes them good candidates for thermal dissipation. The first one consists of a space-filling repetition of a specific unit cell. This repetition pattern is usually made rectilinearly in 3 orthogonal directions, with a cubic unit cell design envelope, and 3 identical constant spacing distances. The properties of TPL with non-rectilinear repetitions [START_REF] Rumpf | Synthesis of spatially variant lattices[END_REF], non-cubic unit cell design envelopes and variable spacing distances have been studied. Contrariwise, stochastic lattices correspond to beam-based structures that do not present any repetition pattern at all. The study of these structures is similar to the one of open-cell foams. Therefore, only triply periodic lattices with parallelepipedic unit cell design envelopes and non-identical constant spacing distances will be considered in this article. It is also established that the use of truss-based lattices is wide spread within the industry sector, due to their earlier emergence and the greater range of available software solutions for their design. This is why the scope of this article has been restricted in this manner. However, the dissipation performances comparison of the proposed trussbased lattices parametrization framework to equivalent work focusing on surface-based structures would be of great interest for a future paper. Like for TPMS, a lot of content can be found on mechanical responses of truss lattices [START_REF] Dong | A survey of modeling of lattice structures fabricated by additive manufacturing[END_REF][START_REF] Rashed | Metallic microlattice materials: A current state of the art on manufacturing, mechanical properties and applications[END_REF], whereas fewer results are related to thermal dissipation [START_REF] Ekade | Fluid flow and heat transfer characteristics of octet truss lattice geometry[END_REF][START_REF] Cheng | Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design[END_REF]. In particular, in case of active cooling, the pressure loss contrasting the use of beam-based lattice structures has been experimentally highlighted [START_REF] Wong | Convective heat transfer and pressure losses across novel heat sinks fabricated by selective laser melting[END_REF]. Moreover, still in case of active cooling, experimental and numerical studies allowed to evaluate the thermal properties of octet-truss [START_REF] Ekade | Fluid flow and heat transfer characteristics of octet truss lattice geometry[END_REF]. Finally, a coupling between topology optimization and lattice structures generation has also been investigated to create complex structures [START_REF] Cheng | Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design[END_REF].

Topology optimized geometries: also called organic structures, these geometries are generated after complex structural computations. Based on Finite Element simulation, topology optimization (TO) consists in numerically removing as much material as possible from an initial design volume, while ensuring that the so-generated part geometry withstands the initially defined load case. Because they are not bound to a geometric family, the way truss or surface-based lattices can be, TO geometries are less constrained: assuming an infinitely small mesh size, the globally optimal geometry for a given problem will be one of the considered solutions. Even if mechanical optimization comes quicker to mind when talking about TO, many thermal TO investigations have been carried out to identify optimal designs of 2D extruded [START_REF] Joo | Topology optimization of heat sinks in natural convection considering the effect of shape-dependent heat transfer coefficient[END_REF][START_REF] Bornoff | An additive design heatsink geometry topology identification and optimisation algorithm[END_REF] and 3D [START_REF] Lazarov | Experimental validation of additively manufactured optimized shapes for passive cooling[END_REF][START_REF] Alexandersen | Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection[END_REF] heat sinks. However, TO still suffers from slow industrialization, because of its significant computation times, its complexity of use requiring a rare expertise, and its expensive software and hardware requirements [START_REF] Dbouk | A review about the engineering design of optimal heat transfer systems using topology optimization[END_REF].

From this literature review, several conclusions can be drawn on the design of heat sinks. First, even if few articles are looking into the use of surface-based lattices to enhance thermal exchanges, exact formulas and parametric optimization have been detailed to optimize the surface area of TPMS. However, no equivalent analysis has been suggested regarding truss lattices. Actually, a lot of effort has been made to study the mechanical characteristics of truss lattices, but few works consider their thermal dissipation potential. Beam-based lattices are perfectly adapted for parametric optimization. They present repetition patterns (unlike open-cell foams or TO geometries), they can be defined by few simple parameters (unlike TPMS) while demonstrating enhanced surface-to-occupancy ratios (compared with pins and fins). All this makes them unquestionably well suited to thermal dissipation.

Overall parametric design framework

The overall framework proposed in this article allows the parametric design and the generation of heat sinks incorporating graded lattice structures for high-performance passive cooling (Fig. 2). It is composed of several steps briefly introduced in the following paragraphs and further detailed in the next sections. Following this process, engineers can modify the values of several control parameters in order to adapt the so-generated lattice structures to their own passive cooling problem. More details are given throughout the paper concerning the influence of each parameter on the resulting lattice-based heat sink geometry.

• Design space definition: from an initial part design (that may or may not already contain a dissipative structure), the design space is delimited, encompassing the maximal volume in which a heat sink structure can be generated. Together with the delimitation of the design space is thus specified a non-design space (or base design) which represents the functional surface and volume of the initial design that must be part of the final geometry to manufacture. Later on, a load case will be defined in order to specify the thermal conditions to be applied to the part.

• Lattice selection and orientation: according to the heat dissipation problem specificities, a unit cell κ is selected, its size a and the beam diameter d must be identified in order to maximize the cooling efficiency, and its orientation parameters o κ have to be tuned in regard to the base design frame in order to further enhance the thermal dissipation. To support decision making in this particular step, engineers can exploit the results and conclusions of the semi-analytic formulation and analysis presented in Section 4.

• Wireframe generation: within the design space, the overall lattice wireframe is first generated, by regularly repeating the corresponding unit cell of size a.

• Lattice volume grading and meshing: once the lattice wireframe has been generated, the diameter of the volume surrounding each skeleton beam must be defined. A vertical gradation can be optionally realized, by defining a diameter value at the interface between the base design and the bottom of the heat sink (d bottom ), and a diameter value at the top of the dissipative structure (d top ). The impact of such a gradation strategy on the overall cooling efficiency is discussed in more detail in Section 5. The meshing of the resulting volume is realized thanks to the marching cubes algorithm, but smarter approaches generating lighter numerical files can be adopted [START_REF] Chougrani | Lattice structure lightweight triangulation for additive manufacturing[END_REF]. • Unification: the meshed heat sink geometry is finally trimmed to the design space delimitation, and merged with the part base design, forming the final part.

Finally, once the final geometric model has been generated, a few preparation steps are still required before its 3D printing: specification of the build orientation, generation of the potential support structures, slice of all the parts to build and selection of the manufacturing parameters.

Unit cells volume density and surface-to-occupancy ratio computation and analysis

This section details the way the volume density and the surface-to-occupancy ratio are computed. The formulas are then analyzed to define design rules helpful to support decision making during the parametric design of high-performance latticebased heat sinks. The considered unit cells are listed in Fig. 3 together with their acronyms. Throughout this article, placed above a particular quantity, the superscript κ is used to highlight that the value is specific to the considered unit cell.

An infinity of other unit cells could be envisioned. However, due to space limitation, only the most common academic and industrial ones are considered in this article [START_REF] Jafari | The utilization of selective laser melting technology on heat transfer devices for thermal energy conversion applications: A review[END_REF]. The overall framework and semi-analytic decomposition strategy remain anyhow valid and replicable for any unit cells.

Semi-analytic unit cell decomposition strategy

To compute the volume density and the surface-to-occupancy ratio of a unit cell, three main approaches can be distinguished. The first one is an analytic approach which consists of computing integrals over intersecting trimmed cylinders, in order to obtain exact formulas. Even though this technique leads to parametric equations which can then be differentiated to identify optimum values, in practice, the equations are complicated to define and to integrate for each unit cell [START_REF] Elmaraghy | Intersection volumes and surface areas of cylinders for geometrical modelling and tolerancing[END_REF].

Another approach is to use a 3D modeling software to generate a series of lattices with various parameter values, and to measure the volume and surface of the generated geometries. Then, a mathematical regression can be performed to identify the equations that drive the evolutions of these two quantities with respect to the lattice parameters. Compared to the analytic approach, this technique is flexible and easily implementable, since the parametric generation of multiple geometries is automated in most existing 3D modelers. However, as demonstrated later on in this article, the volume and surface evolutions of a unit cell are not regular across the whole parametric space. Therefore, the mathematical regression would perform badly in identifying the underlying equations, and would most likely return inaccurate formulas.

As a consequence, the decomposition strategy proposed in this article is a semi-analytic hybrid version of the two previously mentioned techniques. The main idea is to first decompose the unit cell into nodes and beams, as presented in Fig. 4. Indeed, a unit cell can be decomposed into nodes of various topologies and beams of various lengths. The parametrization of the unit cells is realized through two parameters: the side size a and the beams diameter d. For a given lattice structure κ, let us note N κ n the number of node topologies (or types) and N κ b the number of beam types (with different lengths). For instance, when considering the decomposition of the GBCC unit cell of Fig. 4, it comes that

N GBCC n = N GBCC b = 2.
Once the considered unit cell has been decomposed, the volume and surface of each element can be computed independently (Fig. 4). For a beam type j ∈ Moreover, the contribution of each element type to the overall surface and volume depends on its occurrence count. Inspired by the crystallography theory, with each node type (resp. beam type) is associated a specific occurrence count per unit cell ψ κ

Ni (resp. ψ κ Bj ) corresponding to the number of complete nodes (resp. beams) that can be created by assembling all the fraction of nodes (resp. beams) accounted for in the unit cell volume. For example, the top image of Fig. 4 shows a GBCC unit cell composed of 4 vertical beams quarters and 8 horizontal beams quarters having the same length, which gives an occurrence count ψ GBCC B2 = 3 for this particular beam type.

Moreover, with each node type is also associated a valency v κ i (or coordination number or ligancy in crystallography) corresponding to the number of beams connected to this node. For the GBCC unit cell, the valencies of the first and second node types

are respectively v GBCC 1 = 14 and v GBCC 2 = 8.
Once the contribution of each element type is determined, the overall surface S κ and volume V κ of a unit cell can be obtained and used to compute the volume density ρ κ V and surface-tooccupancy ratio ρ κ S as described in Sections 4.4 and 4.5. From those equations, it is then possible to define the diameter-size ratio maximizing the surface-to-occupancy ratio ρ κ S as described in Section 4.7.

Finally, only two parameters (side size a and beams diameter d) are required for a full parametrization of any unit cell κ. This is possible since the lattice structures considered in this article are only presenting Cartesian repetition patterns (so the unit cell remains cubical throughout the repetition). In the case of non-Cartesian lattice structures, more parameters would be needed to define the unit-cell geometry. However, depending on the configurations, the formulas and values obtained for Cartesian repetitions may also remain valid and still very efficient to enhance the thermal dissipation performances in case of non-Cartesian repetition patterns. This is illustrated in Section 5 wherein both categories of repetition patterns have been considered for testing and validation.

Beams length and nodes apparent diameter

The length of the beam type j is defined by the distance between the center of its two extremity nodes. It is proportional to the unit cell side size a. Noting γ κ j this proportionality factor, it comes that:

L κ j = γ κ i a, ∀j ∈ 1; N κ b (1)
Let us also define the apparent diameter d app,i of the node type i, as the minimal distance from which all the connected beams are independent (i.e. are not overlapping). By geometrical considerations, it can be understood that the apparent diameter d app,i is independent of the side size a. Actually, the apparent diameter is only proportional to the beam diameter d, and the proportionality coefficient δ κ i is specific to the node type i of the unit cell κ. The following relation can therefore be written:

d κ app,i = δ κ i d, ∀i ∈ 1; N κ n (2)
Fig. 5 illustrates the node and beam types of each considered unit cell, with their respective occurrence counts, valencies, apparent diameters for the node types, and occurrence counts and lengths for the beam types. One can clearly understand that for the considered unit cells max κ (N

κ n ) = max κ (N κ b ) = 2.
The beam length and node apparent diameter are both used to compute the beams surface and volume analytic contributions in Section 4.5.

Computation of regressions at nodes

In the proposed approach, for a node type, a series of 3D CAD models with various diameters are generated, and their respective volumes and lateral surfaces (without the circular caps resulting from the connected beams trim) are measured. Because the geometry of a node only depends of the beam diameter d, one can understand that modifying this diameter only results in a homothetic transformation (or scaling) of the node. Therefore, because of the linear properties of homothetic transformations, the volume (resp. lateral surface) of a lattice node is proportional to d 3 (resp. d 2 ). Figs. 6 and7 present the volume and lateral surface regressions validating this assumption for the GBCC lattice node of type 1. The points to be fitted have been obtained while measuring the volume (resp. lateral surface) of parametric CAD models. These proportionalities have also been observed for all the other considered unit cells, with Pearson correlation coefficients R 2 above 1 -10 -8 = 0.99999999. Thus, the volume and the lateral surface of a lattice node can be written as:

S κ Ni = α κ i d 2 , ∀i ∈ 1; N κ n (3a) V κ Ni = β κ i d 3 , ∀i ∈ 1; N κ n (3b)
Table 1 lists the values of α κ i and β κ i for the two considered node types, and with respective measurement errors of ±10 -6 and ±10 -8 .

Non-overlapping parametric space

Thanks to the proposed decomposition framework, several lattice parametric design spaces can be identified. Indeed, when increasing the d/a ratio, there exists a certain value σ κ for which the node geometries of the unit cell κ become tangent and start overlapping. This value divides the parametric space into a non-overlapping parametric space (when d/a < σ κ ) and an overlapping one. The delimitation of these two spaces can be visualized in Fig. 8 for the GBCC unit cell.

For the couples of parameters (d, a) in the overlapping parametric space, because the lattice unit cells are only composed of node geometries, Eqs. (3a) and (3b) are not valid anymore. Therefore, the best approach to compute their surface remains the mathematical regression as explained in Section 4.3. However, the overlapping parametric space is mostly composed of closed porosity lattice designs (because of the nodes overlaps) and is thus of less interest for heat sink design. Therefore, in the rest of the paper, only couples of parameters (d, a) in the nonoverlapping space are considered, i.e. for which d/a < σ κ .

Volume density and surface-to-occupancy computation

Using the previously defined notations, in case of a 1 node type and 1 beam type lattice unit cell (N κ n = 1 and N κ b = 1), the surface-to-occupancy ratio ρ κ S and the volume density ρ κ

V are computed as follows:

ρ κ S = S κ V cube = ψ κ N1 α κ 1 d 2 + ψ κ B1 (γ κ 1 a -δ κ 1 d)π d a 3 (4a) ρ κ V = V κ V cube = ψ κ N1 β κ 1 d 3 + ψ κ B1 (γ κ 1 a -δ κ 1 d) π d 2 4 a 3 (4b)
More generally, in case of a unit cell with multiple node types and multiple beam types, the surface-to-occupancy ratio and volume density are computed as follows:

ρ κ S = [ ∑ N κ n i=1 ψ κ Ni α κ i ] d 2 + [ ∑N κ b j=1 ψ κ Bj γ κ j a - ∑ N κ n i=1 ψ κ Ni v κ i δ κ i d
] πd

a 3 (5a) ρ κ V = [ ∑ N κ n i=1 ψ κ Ni β κ i ] d 3 + [ ∑N κ b j=1 ψ κ Bj γ κ j a - ∑ N κ n i=1 ψ κ Ni v κ i δ κ i d ] πd 2 4 a 3 (5b)
Fig. 9 illustrates how these equations are obtained, in the case of a simple 1 node type and 2 beam types lattice structure. The formulas can be simplified as follows: where A κ , B κ , C κ and D κ are constants specific to each unit cell, and defined by the following equations:

ρ κ S = [A κ -C κ ] d 2 a 3 + D κ d a 2 (6a) ρ κ V = [ B κ - C κ 4 ] ( d a ) 3 + D κ 4 ( d a ) 2 (6b)
A κ = N κ n ∑ i=1 ψ κ Ni α κ i , and B κ = N κ n ∑ i=1 ψ κ Ni β κ i (7a) C κ = π N κ n ∑ i=1 ψ κ Ni v κ i δ κ i , and D κ = π N κ b ∑ j=1 ψ κ Bj γ κ j (7b)
Finally, one can notice that the edge effects arising from the trim of the structure to its design space envelope are not taken into account. Indeed, the contribution of the lateral trimmed areas to the overall lattice surface is negligible when considering thousands of repeated unit cells.

Manufacturing requirements

Even if the design freedom provided by AM technologies allows the fabrication of intricate lattice structures, there still exist geometric constraints that need to be met and which are specific to each AM technology. In this paper, the considered manufacturing technology for the fabrication of the heat sinks is Laser Beam Melting (LBM).

An important constraint in LBM is the minimum feature size, and specifically for lattice structures, the minimum manufacturable beam diameter. Even if it varies according to the adopted printing material, machine and manufacturing parameters, it is usual to take d min = 0.5 mm. Another consideration when designing a part for LBM production is the overhang angle. This constraint states that any feature longer than the maximal overhang length ℓ ov , and forming an angle with respect to the build platform lower than an overhang angle θ ov , must be supported [START_REF] Vaissier | Genetic-algorithm based framework for lattice support structure optimization in additive manufacturing[END_REF].

As for the minimum beam diameter, it varies according to the adopted material-machine-parameters tryptic, but common values are θ ov = 45 • and ℓ ov = 1 mm. As a conclusion, the considered unit cells are not manufacturable for any couple (d, a) in the parametric space. The couples (d, a) for which the lattice structure is printable depend on the printing orientation (or balancing) of the whole part. However, as explained in Section 4.7, it is advantageous for passive heat sink design to manufacture lattices with small beam diameters d and small unit cell sizes a. For small values of these two parameters, lattice structures are manufacturable for almost any orientation.

Surface-to-occupancy ratio ρ κ

S maximization

Eqs. (6a) and (6b) show that the volume density ρ κ V is a thirddegree polynomial of the ratio d/a, whereas it is not the case for the surface-to-occupancy ρ κ S . However, for a constant unit cell size a, the surface of a truss lattice is a quadratic function of d, where the second-order coefficient is A κ -C κ . Actually, this coefficient is always negative. This can easily be visualized with the 3 last miniatures of Fig. 9. The surface of a lattice node is smaller than the sum of all the surfaces of the cylinders whose union are forming the lattice node. The same consideration can be made for the volume of the lattice node, which implies the two following inequalities:

C κ > A κ and C κ 4 > B κ (8)
Thus, for a constant value of a, the surface-to-occupancy function presents a maximum. The value of d for which this maximum is reached can be identified by partially differentiating equation (6a) with respect to d, and by finding the value of d for which it vanishes. The diameter-size relation maximizing the surface-to-occupancy ratio ρ κ S is therefore defined by:

∂ρ κ S ∂d = 0 ⇔ d a ⏐ ⏐ ⏐ ⏐ (ρ κ S ) max = Ω κ a = D κ 2(C κ -A κ ) (9)
If this condition is satisfied, by injecting it in Eq. (6a), the surface-to-occupancy ratio maximal value, noted (ρ κ S ) max , can be expressed in two different ways:

(ρ κ S ) max = Φ κ a,a × 1 a with Φ κ a,a = D κ 2 4(C κ -A κ ) (10a) = Φ κ a,d × 1 d with Φ κ a,d = D κ 3 8(C κ -A κ ) 2 (10b)
Fig. 10 shows the evolution of ρ κ S according to the GBCC unit cell parameters. One can clearly see both the curve characterizing the maximum of ρ κ S defined for the specific value Ω κ a of the ratio d/a, and the curve bounding the non-overlapping parametric space defined for the specific value σ κ of the ratio d/a.

A similar analysis could be performed for a constant value of d. Indeed, there exists a value of a maximizing the surfaceto-occupancy ratio ρ κ S . Likewise, this value can be identified by partially differentiating equation (6a) with respect to a. This leads to a different d/a ratio, noted Ω κ value of the other parameter, thus maximizing the surface-to-

occupancy ratio ρ κ S .
Table 2 gathers all the values of Ω κ a and Ω κ d for the considered lattice structures. The errors lie in between 10 -6 and 10 -8 , which is very low, and this proves that the adopted semi-analytic decomposition strategy is valid. Of course, during the parametric design, when tuning their parameters, designers do not need that much accuracy and some values will be rounded. Fig. 11 displays the evolutions of Eq. (10b) for the considered unit cells, i.e. the surface-to-occupancy evolutions according to the beam diameter d, in the case where d/a follows Eq. ( 9). On this figure is also displayed in red the values of d unsuited for LBM production (d < d min = 0.5 mm).

Finally, maximizing the surface-to-occupancy ratio is useful for a heat dissipation problem with a fixed design space. However, for applications such as aerospace or automotive, one other crucial constraint is the weight of the heat sink, which can directly be correlated to the volume densities ρ κ V of the unit cells. Thus, to further characterize the performance with respect to weight issues, the values of ρ κ V must be computed when the respective surface-to-occupancy ρ κ S ratios are maximized. It means that the ratio d/a is constant and follows Eq. ( 9). Because the volume density of a particular lattice is a third-order polynomial of ratio d/a, when Eq. ( 9) is met, the volume density ρ κ V of the unit cell κ is constant. When considering the design scenario for which a is constant, the value of ρ κ V can be obtained by injecting the value of Ω κ a into Eq. (6b). Reversely, for the scenario with d constant, Ω κ d has to be used. Table 3 lists the constant values of ρ κ V , when the respective surface-to-occupancy ratios are maximized for the two design scenarios (i.e. a or d specified by the designer). This table helps the designer in identifying the most suited unit cell when considering the weight constraint.

Synthesis

The equations of the surface-to-occupancy ratio and volume density of any unit cell have been formulated, and numerical values have been computed for the most common ones. Using these results, and depending on their design requirements, engineers can select an appropriate unit cell and tune its control parameters (a, d) to maximize the surface-to-occupancy ratio, and remain in the manufacturable area as well as in the non-overlapping parametric space. Moreover, this parametric analysis leads to the following findings:

• Two design scenarios can be followed and lead to the use of different coefficients: when the designer decides to fix the value of the cell size a, then he/she has to find the value of

d using Ω κ a , reversely if d is fixed, then a is obtained with equation a = d/Ω κ d . • If the couple (a, d) is chosen such that d/a = Ω κ a or d/a = Ω κ
d , then necessarily d/a < σ κ and the node geometries are not overlapping. This is straightforward when analyzing the relative position of the two curves of Fig. 10.

• The BCCxyz unit cell reveals a slightly higher surface-tooccupancy ratio than the others. This is thus the one selected for the experimentations and for the validation in Section 5.

Finally, the formulas and findings presented in this section are valid for Cartesian lattice structures, and this covers most of the industrial situations. However, the overall framework and the semi-analytic decomposition scheme remain adapted for non-Cartesian repetition patterns. In this case, new parameters would notably appear and the formulas would significantly change.

Experimentations and results

The parametric analysis performed on various unit cells has demonstrated the existence of an optimal ratio d/a that maximizes the surface-to-occupancy ratio of the structure. However, even though it is straightforward that the thermal exchange surface has an important impact on the performances of a passive dissipative structure, it is not the only parameter that can influence them. This section considers a design scenario for which a is fixed by the designer. It demonstrates through numerical experiments that a lattice structure generated with the previously identified d/a = Ω κ a value is indeed the optimal structure considering the thermal dissipation performances. It also shows that the findings obtained for Cartesian repetition patterns may still be of interest to enhance the thermal dissipation performances of non-Cartesian lattice structures.

Numerical validation on an academic test case

The experiments and the numerical validation have been realized on an academic test case, represented by a 0.5 mm thick plate, shaped like a square of 10 mm side. The thermal load case consists of a 5 W heat flux applied at the bottom face of the plate. All the dissipative structures compared in the following paragraphs are encompassed in a 10 mm side cube located above the top face of the plate, which corresponds to the heat sink

Table 4

Parameters used for the simulation of the academic test case.

Simulation parameters

Thermal conductivity of solid material λ

148.62 W m -1 • C -1 Convective heat transfer coefficient 10 W m -2 • C -1 Ambient temperature 20 • C
design space. The material chosen for the simulations is Aluminum. Indeed, it is a common AM printing material, presenting great thermal properties. This article focuses on passive cooling applications, and the simulations are thus realized accordingly: the conduction of the heat through the solid material (namely the lattice structure) is modelized along with the heat convection between the solid material and the surrounding air. Specifically, the thermal conductivity within the solid material is proportional to the temperature gradient within the lattice structure, and the convection between the lattice structure and the surrounding air (modelized through the convective heat transfer coefficient) is proportional to the temperature difference between the solid material and the fluid. The performance of a particular dissipative structure is measured through the maximal temperature T max of the whole part when the steady state is reached. These simulations have been realized with Ansys Discovery Live, using the parameters listed in Table 4.

Following the proposed parametric design framework, once the design space is defined, the next step consists in selecting the unit cell (Fig. 2). Here, the BCCxyz unit cell has been selected since, as visible in Fig. 11, it presents the highest surface-tooccupancy maximal value (ρ κ S ) max for the considered scenario (i.e. a constant value of a).

As a reminder, the scope of this article is to consider a static heat dissipation problem. However, even for a non moving part without any fluid stream generating device, one cannot completely ignore the existence of a fluid flow circulating through the heat sink structure. Keeping in mind this element, the best orientation for the adopted lattice structure is selected. For the BCCxyz unit cell, Fig. 13 illustrates three possible orientations in the case of a fluid flow perpendicular to the figure plane. It clearly shows that the isometric orientation (c) is the one with the largest pores, letting more easily the surrounding fluid go through the dissipative lattice structure. This is therefore the o κ orientation adopted for the generation of the BCCxyz lattice structure. As it will be shown in the next subsection, this ideal orientation can be used to drive the generation of the entire wireframe while following both linear and curved repetition paths.

The first set of simulations are realized on non-graded lattice structures, with constant unit cell size a = 1.83 mm, such as the one of Fig. 12.c. Indeed, this is the value of the unit cell size for which the optimal beam diameter d is equal to Ω κ a ×a = 0.5 mm. To demonstrate the optimality of this beam diameter value, the simulations are realized on structures presenting various beam diameters d, ranging from 0.4 mm to 0.6 mm. In Fig. 14 representing the output results of these simulations, one can see that the minimal value for T max is indeed obtained when the beam diameter d = 0.5 mm. These results demonstrate that choosing the right set of values for the parameters couple (a, d) leads to the best thermal dissipation performances, in the case of a non-graded lattice design. The resulting temperature T max is also compared to the ones obtained in the case of fin-based and pin-based dissipative structures (Fig. 12.a to c). The feature sizes of these structures have been defined equal to the beam diameter of the compared lattice structure, specifically 0.5 mm, for the comparison to be fair. The differences between the T max values of the three first simulations of Fig. 12, clearly illustrate the interest of using a well parametrized lattice-based structure for static heat dissipation applications. However, in a passive thermal dissipative problem, heat conduction through the solid material plays an important part in the obtention of the best performances. By homogenizing the distribution of the heat throughout the whole geometry of the heat sink, one can increase the overall thermal exchanges with the surrounding fluid and enhance the general performance of the dissipative structure. This is characteristic of thermal Topology Optimization results, generally demonstrating massive trunks at their base, with thinner ramifications as the structure grows away from the heat source. In the case of a lattice structure, this variation of volume density enhancing the thermal conductivity can be realized through a gradation of the beam diameter, from the bottom to the top of the dissipative structure. In case of a linear gradation strategy, two diameter values are needed, namely d bottom and d top , with d bottom ≥ d top . While keeping d top to its minimum manufacturable value of 0.5 mm, several test geometries have been simulated by varying the value of d bottom from 0.5 mm to 0.8 mm. However, because the adopted starting beam diameter value (d top = 0.5 mm) maximizes the surface-to- occupancy ratio, this gradation is realized at the expense of the exchange surface of the structure. This is why, analyzing the measured values of T max for each of the simulations plotted in Fig. 15, one can see that only a slight gradation of the beam diameter over the height of the lattice structure uniformizes indeed the temperature distribution throughout the structure, enhancing its thermal dissipative properties. Formulated differently, the tradeoff made on the surface exchange to ensure a better temperature distribution quickly becomes unfavorable with respect to the thermal dissipation performance of the whole structure. From Fig. 15, a d bottom = 0.53 mm appears to be the best compromise, and this value will therefore be adopted for the gradation of the industrial test case. Such a low-amplitude gradation (d ∈ [0.5..0.53]) can hardly be visually detected. Thus, to see the gradation, the simulation of Fig. 12.d has been performed using a higher gradation amplitude (d bottom = 0.8 mm) and it corresponds to the one on the right of Fig. 15, thus resulting in a higher T max value.

Industrial case studies

Two different industrial case studies are considered for testing and validation: the redesign of an oil tank carter and of a bent pipe. The first case study requires Cartesian repetition patterns, whereas the second makes use of non-Cartesian lattice structures. Hot oil is circulating under the carter and inside the pipe, and needs to be cooled down. In both cases, the constant heat flux that needs to be dissipated is equal to 15 W, and the parameters used for the simulations are the ones used for the academic test case (Table 4). Fig. 16.a presents the initial design of the carter. On this design version, the heat dissipation is thus realized through thin fins located above the carter. Following the proposed design framework, a maximal design space is first delimited from the initial design (Fig. 16.a), with the carter base blank of any heat dissipation structure. According to the parametric analysis of Section 4.5, a wisely parametrized lattice-based heat sink is generated above the carter base (Fig. 16.b), and its dissipation performances are compared to the ones of the initial design. The lattice unit cell adopted for this industrial case study is still the BCCxyz, oriented identically as for the academic test case. The generation of the lattice wireframe is realized within the pre-defined design space, along the main Cartesian directions, with a unit cell size equal to 1.83 mm. Overall, 146 629 beams are generated. A graded volume is then generated around the wireframe, with an optimal d bottom value equal to 0.53 mm and d top still selected at the limit of the manufacturing possibilities (d top = 0.5 mm). These values are adopted based on the previously analyzed simulations of Fig. 15, demonstrating that a low gradation is preferential with small beam diameter values. The simulation result of the redesigned version of the carter is compared to the one of the initial version that uses vertical dissipative fins (Fig. 17). One can clearly see that T max has significantly been reduced from 81.3 • C to 54.6 • C. This comparison validates the proposed approach for the design of high-performance heat sinks.

The proposed parametric design approach has also been followed to improve the design of a bent pipe. The initial design is made of 32 fins surrounding the pipe and bent to follow the evolution of its shape. The simulation result of this initial design highlights a T max = 76.1 • C (Fig. 18.a). Starting from this version, a pre-defined design space is identified and filled in with a lattice structure whose repetitions follow the shape of the bent pipe. Overall, 64 320 beams are generated with a unit cell size equal to 1.83 mm and a constant beam diameter of 0.5 mm. To follow this curved non-Cartesian repetition pattern, each unit cell is slightly stretched and rotated along the path. Here again, when compared to classical fins, the simulation results clearly demonstrate the interest of using truss lattice structures for the design of high-performance heat sinks (Fig. 18.b). This example also shows that, even though the adopted parameters a and d cannot be anymore considered as optimal (because the formulas used to obtain them are valid for Cartesian repetition schemes), their use still helps to improve the overall performance of the heat sink. Actually, in the present case, the unit cells are not stretched that much as the angular variation between two neighbor cells does not exceed 4.1 • . Thus, using the formulas obtained for Cartesian repetitions can still be considered as a good approximation. Of course, while defining a proper parametrization of this particular example, and while identifying the corresponding new formulas, one could find out new optimal values for the unit cells parameters so as to further improve the thermal dissipation performances.

Conclusions and future works

This article has introduced a new framework for the parametric design of graded truss lattices that maximize passive cooling. The geometry of these intricate structures is controlled by several parameters related to the type of unit cell κ used to populate a design space, the unit cell size a and beam diameter d, its orientation parameters o κ in regard to the base design frame, the gradation parameters d top and d bottom . A semi-analytic decomposition strategy has been proposed to study the volume density and the surface-to-occupancy ratio of state-of-the-art unit cells. In particular, a parametric analysis (whose parameters were the beam diameter d and the unit cell size a of the lattice structure) allowed to identify the underlying equations followed by these two quantities. The values Ω κ a (resp. Ω κ d ) of the ratio d/a that maximize the surface-to-occupancy ratio of each unit cell have been identified and should be used when the designer fixes the cell size a (resp. the beam diameter d). The experimentations and results have shown that the proposed approach helps designing lattice-based heat sinks with enhanced thermal dissipation performances, compared to traditional fins-based geometries. Even though the perimeter of this paper has been restricted to Cartesian lattices, the proposed approach can easily be extended to structures presenting non-Cartesian repetition patterns. An example of such a possibility has been presented where the unit cells are stretched and rotated along free-form curves. Actually, when considering slight shape deviations from a perfectly cubic unit cell, the formulas obtained for Cartesian repetition schemes can still be considered as a good approximation.

The scope of this article was restricted to the case of passive cooling. Because of their low manufacturing costs and maintenance requirements, static heat sinks are widely used. However, for specific applications involving high heat generation sources, the performances can be greatly enhanced by the presence of a naturally or artificially induced fluid stream through the heat sink.

In the case of such an active heat dissipation problem, the present study is a great starting point and, through the proposed framework, designers still have access to all the control parameters. Indeed, maximizing the exchange area between the heat sink and the surrounding fluid is still a crucial aspect in such configuration. The beam diameter over the unit cell size ratio maximizing the surface-to-occupancy ratio, namely Ω κ a or Ω κ d , gives therefore a first part of the solution. However, selecting d as low as possible with respect to the manufacturing capabilities is not the best approach anymore. The two parameters d and a being coupled through the value of Ω κ a or Ω κ d , the smaller d is, the smaller the pores of the lattice structure are, preventing the fluid stream from correctly circulating through the heat sink (a phenomenon known as pressure loss). Another parametric analysis of the pressure loss of a specific lattice according to the same parameters a and d would enable the identification of another optimal couple (d, a). Furthermore, according to their orientation o κ , some lattice unit cells are demonstrating bigger pores with respect to a and d. Thus, prioritizing the selection of a lattice unit cell κ with a higher pore size with respect to a and d, but with a slightly lower surface-to-occupancy ratio might be preferential for an active heat dissipation problem.

Finally, this paper has been focusing on optimizing the surface-to-occupancy ratio of truss-based lattice structures. However, multi-objective problems can arise when trying to resolve heat dissipation problems, in particular when the volume or the structural response of the resulting dissipation structure must be controlled. Since analytic formulas of truss-based lattices surfaces have been provided in this paper, the extension of this work to multi-objective optimization will be facilitated for future works.

Fig. 1 .

 1 Fig. 1. Heat sinks designed by means of traditional fins (a), or incorporating a graded truss lattice structure (146 629 beams) for enhanced heat dissipation (b).

Fig. 2 .

 2 Fig. 2. Overall framework for the parametric design and the generation of high-performance heat sinks incorporating graded lattice structures.

Fig. 3 .

 3 Fig. 3. Considered state-of-the-art unit cells and their acronyms.

Fig. 4 .

 4 Fig. 4. Decomposition strategy for the computation of the volume density and surface-to-occupancy semi-analytic formulas (κ = GBCC ).

Fig. 5 .

 5 Fig. 5. The considered unit cells and cross-section views, together with the corresponding occurrence counts ψ κ Ni , valencies v κ i and apparent diameters d app,i for each

Fig. 6 .

 6 Fig. 6. Surface regression of the GBCC lattice first node geometry.

Fig. 7 .

 7 Fig. 7. Volume regression of the GBCC lattice first node geometry.

Fig. 8 .

 8 Fig. 8. Separation of parametric spaces for the GBCC unit cell.

Fig. 9 .

 9 Fig. 9. Visual details of the surface S κ and volume V κ computation around a node in case of a simple 1 node type and 2 beam types lattice structure.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Evolution of the surface-to-occupancy ratio of the GBCC unit cell highlighting the value Ω κ a of d/a for which ρ κ S is maximum (scenario a is constant), and the value σ κ of d/a which characterizes the limit of the non-overlapping parametric space.

d

  , and different values of the coefficients Φ κ d,a and Φ κ d,d used to compute (ρ κ S ) max . Due to space limitations, these equations are not provided here. Depending on the encountered scenario, i.e. whether the engineer chooses to fix the value of a or the value of d, either the coefficient Ω κ a or Ω κ d must be used to determine the optimal

Fig. 12 .

 12 Fig. 12. Simulation results for the academic test case with pin-based (a), fin-based (b), regular oriented lattice (c), and graded oriented lattice (d) dissipative structures.

Fig. 13 .

 13 Fig. 13. Front (a), side (b) and isometric (c) views of BCCxyz unit cell.

Fig. 14 .

 14 Fig. 14. Maximal temperature in the regular lattice of the academic test case when steady state is reached according to the beam diameter d.

Fig. 15 .

 15 Fig. 15. Variation of the maximal temperature T max according to the d bottom value of graded lattice structures (d top = 0.5 mm).

Fig. 16 .

 16 Fig. 16. Initial design and deduced design space of an industrial oil tank carter (a), and graded oriented lattice-based heat sink (b).

Fig. 17 .

 17 Fig. 17. Simulations of the initial (a) and final (b) designs of the industrial carter case study.

Fig. 18 .

 18 Fig. 18. Simulations of the initial (a) and final (b) designs of the industrial bent pipe case study.

Table 1

 1 Proportionality coefficients α κ i and β κ i for the lateral surface and volume of the considered unit cells.

	Acronym (κ)	α κ 1	β κ 1	α κ 2	β κ 2
	G	0.939514	0.94198377	N/A	N/A
	BCC	3.074558	1.99338745	N/A	N/A
	OT	3.677716	3.33365169	N/A	N/A
	D	0.768658	0.49835000	N/A	N/A
	BCCz	8.155219	3.88799115	N/A	N/A
	BCCxyz	5.306663	4.42474702	N/A	N/A
	FCC	3.677737	3.33365520	2.283168	0.90412690
	GBCC	5.306663	4.42474702	3.074558	1.99338745
	GFCC	11.774450	7.65076508	2.283168	0.90412690

Table 2

 2 Values of Ω κ

	Acronym (κ)	Ω κ a	Ω κ d
	G	0.55536151	0.74048200
	BCC	0.37023936	0.49365247
	OT	0.230036924	0.306715899
	D	0.3702412	0.4936549
	BCCz	0.31600360	0.42133813
	BCCxyz	0.273120323	0.364160430
	FCC	0.32532145	0.43376193
	GBCC	0.30063617	0.40084823
	GFCC	0.26342710	0.35123614

a and Ω κ d maximizing the surface-to-occupancy ratio.

Table 3

 3 Volume densities which maximize surface-to-occupancy ratios.

	Acronym (κ)	ρ κ	d
	G	48.4%	71.4%
	BCC	49.7%	73.7%
	OT	47.0%	69.7%
	D	49.7%	73.7%
	BCCz	46.7%	69.2%
	BCCxyz	50.5%	74.8%
	FCC	47.0%	69.7%
	GBCC	47.0%	69.6%
	GFCC	41.7%	61.8%

V when d/a = Ω κ a ρ κ V when d/a = Ω κ


Alan R Hevner
email: ahevner@usf.edu

Nicolas Prat
email: prat@essec.edu

Isabelle Comyn-Wattiau

Jacky Akoka
email: jacky.akoka@cnam.fr

Pre

Keywords: Design Science Research, Goals, Fitness, Evolution, Innovation

The effectiveness of a Design Science Research (DSR) project is judged both by the fitness of the designed artifact as a solution in the application environment and by the level of new research contributions. An important and understudied challenge is how to translate DSR project research goals into discrete and measurable evaluation criteria for use in the DSR processes. This position paper proposes an inclusive approach for articulating DSR goals and then identifying project evaluation criteria for these goals. The goals are organized hierarchically as utilitarian goals, safety goals, interaction and communication goals, cognitive and aesthetic goals, innovation goals, and evolution goals. Goals in a DSR project are identified pragmatically by considering the components of the context coupled with the hierarchy of goals. Based on the identified goals, the associated evaluation criteria are determined and organized along the same hierarchy. These criteria measure the ability of the artifact to meet its goals in its context (immediate fitness). Moreover, our approach also supports the innovation and research contributions of the project. The apex of the goal hierarchy addresses the identification of criteria measuring the fitness for evolution of the designed artifact, to accommodate for changes in goals or context.

Introduction

Design science research (DSR) projects seek to solve interesting problems via innovative artifacts that contribute new knowledge to the world. Among the key research challenges is the ability to understand and define the goals of the DSR project and how to determine whether and to what extent such goals are met. Multiple design cycles of build and evaluate activities strive to produce the design artifacts that provide both a satisfactory solution to the problem and the contribution to the research knowledge base [START_REF] Simon | The Sciences of the Artificial[END_REF][START_REF] Hevner | Design Science in Information Systems Research[END_REF]. It is the rigorous evaluation of the DSR artifacts that determines if research goals are met.

2

The identification of DSR goals and their transformation into well-defined and measurable evaluation criteria remains an understudied topic. How do we evaluate the "goodness of fit" of a designed artifact as a solution in an application environment? How do we rank potential design candidates so as to select the best one for implementation as a solution? How do we capture and represent the new research contributions (e.g. design theories) of an innovative artifact in order to add them to the knowledge base? Such questions require the DSR project team to define the evaluation criteria for the project and design the rigorous methods for evaluating the design artifacts under these criteria. The rigor and credibility of a DSR project is determined by these evaluation decisions.

In the Information Systems field, several models of DSR evaluation methods have been proposed. [START_REF] Venable | FEDS: a Framework for Evaluation in Design Science Research[END_REF] present a framework of artifact evaluation comprising two dimensions -naturalistic vs. artificial and ex ante vs. ex post. Naturalistic evaluation is done in real world environments while artificial evaluation is performed in more controlled "laboratory" settings. Ex ante evaluation is formative, performed during the build and evaluate design cycles, while ex post is summative, performed after the artifact build is complete. The authors propose and plot evaluation strategies along the two-dimensional grid. [START_REF] Sonnenberg | Evaluations in the Science of the Artificial -Reconsidering the Build-Evaluate Pattern in Design Science Research[END_REF] propose a framework with four different stages of evaluation in a DSR project. Different evaluation methods are used in problem identification, solution design, artifact instantiation, and solution in use. [START_REF] Prat | A Taxonomy of Evaluation Methods for Information Systems Artifacts[END_REF] perform an extensive literature review of DSR projects and produce a taxonomy of evaluation methods. A key insight from this study is the limited scope of evaluation criteria applied across the reported DSR projects. Most previous DSR studies have stated high-level evaluation criteria in such terms as artifact effectiveness, utility, validity, or other general concepts that are difficult to define and measure [START_REF] Prat | A Taxonomy of Evaluation Methods for Information Systems Artifacts[END_REF]. We observe that none of the studies provide detailed guidance to determine the evaluation criteria for a given DSR project's goals.

Our objective in this paper is to present initial thinking toward the development of a pragmatic approach for determining the research goals of a DSR project and transforming those goals into a well-defined set of criteria for use in the formative and summative evaluations of the design artifacts. A DSR project aims at building an artifact that provides a solution to a problem while adding new knowledge to the world. A problem is characterized by goals identified in a context. Evaluation criteria not only assess to what extent the artifact meets the goals in the context (immediate fitness), but also to what extent it can accommodate changes in goals or context (fitness for evolution). Central to our approach is a hierarchy of DSR goals. Coupled with the context, this hierarchy guides the identification of DSR goals. From there, evaluation criteria are identified via use of the same goal hierarchy.

The rest of the paper is organized as follows. Section 2 presents the basic building blocks of our approach: problem context, goals, and evaluation criteria. We propose a six-level hierarchy of goals as a way to organize the new approach. Section 3 reviews past literature for examples of evaluation criteria that fit into the goal hierarchy. Section 4 presents a model of the DSR processes that incorporates our new pragmatic approach for applying the goal-driven evaluation criteria in DSR project design cycles. We complete the paper with our conclusions and future research directions in Section 5.

2 Context, Goals, and Evaluation Criteria

DSR projects solve an important problem in a defined application domain. A detailed understanding and description of this problem are essential to provide a convincing relevance for the research project. Two key components comprise a project's problem space -the application context (including the environment) and the goals for solution acceptance. In the remainder of this section, we establish a foundation for our proposal by providing a brief review of these basic terms in a DSR project.

Context

The environmental context provides a rich understanding of the problem space. Typically, design artifacts are situated in an organizational context, and their immediate environment is composed of people, organizations and technology [START_REF] Hevner | Design Science in Information Systems Research[END_REF][START_REF] Sjöström | Designing Information Systems -a Pragmatic Account[END_REF]. Important pragmatic questions are: What is the application domain and what is the current state of design knowledge (e.g. existing artifacts and design theories in use) for this domain? Who are the key stakeholders in the problem space who will impact and be impacted by the design solution?

The context includes information on the time and location of the research project. Design solutions reflect the point in time when they are designed. Available technologies, scientific theory bases, government regulations, national and international laws, and societal mores change over time. Therefore, a clear fixing of the time during which the research is conducted is essential to support both immediate fitness and fitness for evolution. Contextual aspects of location include the relevant geographic particulars such as rural vs. urban environments or developed vs. developing countries. As an example, one formal approach for describing the problem context is the PESTLE tool for business analysis [START_REF] Cadle | Business Analysis Techniques -72 Essential Tools for Success[END_REF] with contextual categories of Political, Economic, Socio-cultural, Technological, Legal, and Environmental.

Hierarchy of DSR Goals

In a DSR project, the value of a design artifact is defined by the goodness of its fit as a solution for the problem or opportunity presented. In addition, the design must be novel in a way that adds new knowledge to a growing domain knowledge base. The research challenge is how to express these high-level DSR goals in appropriate ways that can be understood, measured, and communicated to the various stakeholders. Unfortunately, there is little research into the characteristics that provide good estimates of design fitness and novelty. This naturally presents a substantial obstacle to any DSR project that attempts to predict or estimate the success of a particular artifact. The largely unexplored forces driving artifact design fitness and novelty represent a considerable opportunity for research into how best to identify DSR research goals and transform them into defined evaluation criteria.

To guide the identification of DSR goals, we propose to define major categories of goals and organize these categories into a hierarchy. Not only will this hierarchy facilitate the identification of goals, it will also provide a structure for classifying evaluation criteria. The idea here draws on the balanced scorecard [START_REF] Kaplan | The Balanced Scorecard: Translating Strategy into Action[END_REF], which defines four perspectives for identifying business objectives. These perspectives form a hierarchy, so that meeting the objectives at one level contributes to meeting those at the upper level (the top level of the hierarchy being the financial 4 perspective). The perspectives are also used to organize the indicators measuring to what extent the objectives are met.

To define our hierarchy of goals for socio-technical system solutions, we adapt [START_REF] Maslow | A Theory of Human Motivation[END_REF] hierarchy of human needs. Although this hierarchy has sometimes been criticized as stereotypical, it continues to be used frequently in research. The ultimate purpose of artifacts is to serve human needs. However, we need to adapt Maslow's hierarchy to take into account the specificities of DSR artifacts with their socio-technical natures. Maslow's initial hierarchy of needs contains the following levels: physiological, safety, belonging and love, esteem, and self-actualization. These needs form a hierarchy in the sense that a human being needs to fulfill the needs of one level to focus motivation on the needs of an upper level. The original hierarchy was refined into the following hierarchy [START_REF] Maslow | Toward a Psychology of Being[END_REF]) via applications and analyses: physiological needs, safety needs, social needs, esteem needs, cognitive needs, aesthetic needs, self-actualization, and self-transcendence.

In the field of information systems, Urwiler and Frolick ( 2008) use Maslow's hierarchy as a metaphor to gauge the maturity level of Information Technology (IT) in organizations. They propose the hierarchy: infrastructure and connectivity needs, stability and security needs, integrated information needs, competitive differentiation, and paradigm shifting. Moving up this hierarchy means moving from commodity IT to innovative IT.

In marketing, [START_REF] Srinivasan | The Total Product Design Concept and an Application to the Auto Market[END_REF] define the total product design concept (TPDC) as consisting of three elements, namely functionality, aesthetics, and meaning; each of which arises from more elemental product characteristics. Although the TPDC is not directly related to Maslow's pyramid, it provides insights for its adaptation. Functionality refers to the utilitarian dimension of a product. It arises from the product's features and related benefits. Aesthetics is the product's sensorial characteristics and meaning refers to the associations of the product in the minds of its customers.

Thus, based on Maslow's pyramid and the above-mentioned papers, we define the following six-level hierarchy (Figure 1) of DSR goals: (1) utilitarian goals, (2) safety goals, (3) interaction and communication goals, (4) cognitive and aesthetic goals, (5) innovation goals, and (6) evolution goals. We note that physical needs are generally not relevant to DSR artifacts. Instead, utilitarian goals form the base of the hierarchy, corresponding to functionality in the TPDC mentioned above. Placing utilitarian goals at the base of the hierarchy implies that they should be fulfilled in order for upper-level goals to be considered. Interaction and communication goals (similar to the integrated information needs above) correspond to Maslow's social needs. Cognitive and aesthetic goals are placed at the same level (we do not establish a hierarchy between the "beauty" of a demonstration in mathematics and the beauty of a piece of art).

Innovation goals (contributing creative knowledge and artifacts) come next, corresponding to self-actualization in Maslow's hierarchy. Note that self-actualization is the highest level of Maslow's hierarchy of needs that is relevant in DSR (selftranscendence is not applicable). Placing innovation at this high level is also consistent with the hierarchy of [START_REF] Urwiler | The IT Value Hierarchy: Using Maslow's Hierarchy of Needs as a Metaphor for Gauging the Maturity Level of Information Technology Use within Competitive Organizations[END_REF], which reflects increasingly innovative applications of IT in organizations. Finally, evolution (ability to manage change) goals constitute the upper level of the hierarchy. Although Maslow's original hierarchy of needs does not consider evolution, this concept appears in adaptations of the hierarchy. For example, [START_REF] Kiel | Reshaping Maslow's Hierarchy of Needs to Reflect Today's Educational and Managerial Philosophies[END_REF] proposes to represent the hierarchy of human needs as a triangle that is open at the top, reflecting the "boundlessness" of selfactualization: self-actualization is a continuously evolving process.

DSR Project Evaluation Criteria

Upon identifying the goals of a DSR project, the next step is to find evaluation criteria that are instantiated in the artifacts and subsequently measured in the evaluations. In the following section, we pay particular attention to the understudied goals of innovation and evolution [START_REF] Gill | A Fitness-Utility Model for Design Science Research[END_REF]). Consequently, one objective of this paper is to remediate this imbalance and investigate evaluation criteria for innovation and evolution more fully. To this aim, we start by a brief review of evaluation criteria for DSR artifacts, and then dig deeper into the past forms of evaluation for innovation and evolution from multiple fields. We end with an initial proposal for a partial listing of the six levels of evaluation criteria that can be used to measure goal achievement in a DSR project.

Evaluation Criteria for DSR Artifacts

The DSR literature contains a number of proposed approaches for the construction and evaluation of design artifacts and the reflection and guidance on resulting design theories [START_REF] Winter | Design Science Research in Europe[END_REF]. Examples of evaluation criteria proposed in DSR projects are found in [START_REF] March | Design and Natural Science Research on Information Technology[END_REF][START_REF] Hevner | Design Science in Information Systems Research[END_REF][START_REF] Sonnenberg | Evaluations in the Science of the Artificial -Reconsidering the Build-Evaluate Pattern in Design Science Research[END_REF][START_REF] Gregor | Positioning and Presenting Design Science Research for Maximum Impact[END_REF][START_REF] Baskerville | Genres of Inquiry in Design-Science Research: Justification and Evaluation of Knowledge Production[END_REF]. In particular, [START_REF] Prat | A Taxonomy of Evaluation Methods for Information Systems Artifacts[END_REF] propose a taxonomy of evaluation methods for IS artifacts, with a special focus on evaluation criteria. This taxonomy is based on a literature review of design science papers, coupled with an in-depth content analysis of 121 DSR papers. The content analysis reveals a focus on a few assessed criteria being (in descending order) efficacy, usefulness, technical feasibility, accuracy, and performance. We find that the evaluation criteria addressed in these papers primarily address the lower levels of 6 DSR goals in our goal hierarchy, more specifically utilitarian goals with some discussion of safety and interaction/communication goals. In the next sections, we focus on the underexplored goal categories of innovation and evolution.

Innovation Evaluation Criteria

The innovation goals of a DSR project are especially challenging to identify and structure as evaluation criteria. Important guidance for understanding the DSR problem space and establishing innovation goals comes from [START_REF] Gregor | Positioning and Presenting Design Science Research for Maximum Impact[END_REF][START_REF] Gregor | The Knowledge Innovation Matrix (KIM): A Clarifying Lens for Innovation[END_REF] via the Knowledge Innovation Matrix (KIM). KIM (Figure 2) is structured on the most fundamental feature of innovation -new knowledge created and applied in some tangible form to achieve human goals. The tangible forms that innovations take include products, processes, and services. Taking knowledge and its application (to human needs) as the keys to understanding innovation means that many other labels and categorizations that only partly deal with the innovation space are encompassed: ideas, creativity, technological know-how, products, competencies, organizational learning, and exploration versus exploitation [START_REF] March | Exploration and Exploitation in Organizational Learning[END_REF][START_REF] Tidd | Managing Innovation Integrating Technological, Market and Organizational Change[END_REF]. That knowledge is the key feature in all of these terms is apparent on reflection. Companies do not value the innovative products they produce so much in themselves as the knowledge assets they embody. After all, they sell these products to consumers. What they value is the knowledge asset represented in the product -the intellectual property that may be worth protecting by patents, trade secrets, and/or copyrightsincluding the need it meets. A DSR project will position its innovation goals in one of the three research quadrants of invention, advancement, and exaptation. The selected quadrant provides guidance on the types of research contributions to be made and how these contributions will be communicated and evaluated. A recent editorial presents a detailed discussion of DSR contributions on finding the right balance between the design artifact and the design theories [START_REF] Baskerville | Design Science Research Contributions: Finding a Balance between Artifact and Theory[END_REF]. The key observation is that DSR contributions form a continuum on at least two dimensions: from very novel artifacts to rigorous theory development and from early visions of technology impact to studies of technology impact on users, organizations and society. Thus, there can be multiple types of published contributions depending on the novelty of the artifact and the phase of the research project. Evaluation criteria for innovation will be the evidence of new artifacts, new theories, and the impacts of these novel contributions. We find several examples of proposed evaluation criteria for DSR innovation in [START_REF] Baskerville | Genres of Inquiry in Design-Science Research: Justification and Evaluation of Knowledge Production[END_REF] with innovativeness and inventiveness and [START_REF] Gill | A Fitness-Utility Model for Design Science Research[END_REF] with novelty.

Evolution Evaluation Criteria

As a central premise of our research direction we contend that over time the evolutionary goals of design artifacts become far more interesting than the use fitness of a particular artifact at a static point in time. The validity of this premise is likely to depend on the problem space in which it is situated. For very static environments, for example, a particular artifact may exist for a very long time with high capability. In this situation, the immediate fitness of the artifact is a matter of considerable interest. In a highly dynamic environment, however, the artifact's potential to evolve needs to be given much greater weight. The benefits of encouraging diversity and openness of designs as insurance against major changes in the problem (goals or context) would be of paramount importance. Our belief is that such dynamism describes most environments facing designers of socio-technical systems today and forces such as globalization, energy conservation, social media, and advances in telecommunications will likely serve to increase such environmental turbulence.

Closely aligned to our approach, Gill and Hevner (2013) explore a design fitness and utility function of DSR artifacts, drawing on the fields of biology and economics. Fitness is not directly observable and is assessed with a utility function, based on a set of attributes of design artifacts, termed design traits (in essence, evaluation criteria). The authors identify and illustrate eight key design traits: usefulness, decomposability, malleability, openness (e.g., open source), embeddedness in a design system (e.g., the design ecosystem of Apple), novelty, interestingness, and elegance.

In the field of software engineering, [START_REF] Lehman | Laws of software evolution revisited[END_REF] identifies eight laws of software evolution: (I) continuing change, (II) increasing complexity, (III) selfregulation, (IV) conservation of organizational stability (invariant work rate), (V) conservation of familiarity of all involved with the software's goals, (VI) continuing growth, (VII) declining quality, and (VIII) feedback system. These eight laws are grounded empirically, i.e. resulting from observation. We find limited follow up in the software engineering literature to these early empirical results.

In the systems engineering field, [START_REF] Sauser | Systomics: The Ultimacy of Design[END_REF][START_REF] Sjöström | Designing Information Systems -a Pragmatic Account[END_REF] contend that there is a molecular level below General Systems Theory that is not fully discovered or defined. They call it systomics, the study of a system's DNA. Fundamental system characteristics in systomics are autonomy, belonging, connectivity, diversity, and emergence. In marketing, [START_REF] Srinivasan | The Total Product Design Concept and an Application to the Auto Market[END_REF] propose the concept of "total product design" which contains elements of continuous evolution of the product.

In IS, [START_REF] Agarwal | Editorial -Evolvable systems: Through the Looking Glass of IS[END_REF] explore evolvable systems, understood as software-based information systems. They define the evolvability of a system as its capacity to efficiently serve new purposes and emerging possibilities. They argue that systems evolvability is an important and underexplored topic since most IS research generally focuses on the first use of a software system and the phases that precede it, not on evolution that takes place afterwards. They propose some proxies to assess systems evolvability: plasticity, boundary morphing (temporal change in the proportion of functionalities implemented within the system vs. those accessible via APIs), mortality, market durability, mutation, pleiotropy (production of more than one effect, e.g. genes having multiple phenotypic expressions), and interoperability.

Mapping of Evaluation Criteria to DSR Project Goals

In this position paper, our objective is not to produce an exhaustive list of all possible evaluation criteria for a DSR project to consider. In the Appendix, we present a proposed list of criteria that have been identified in the above literature review as a starting point for transforming DSR goals into specific evaluation criteria. For each evaluation criterion, Table A shows the definition of the criterion with the source or sources from which the definition was taken or adapted. In this section, we bridge the gap between the hierarchy of goals and evaluation criteria identified above, by using the hierarchy of goals to organize the sample of evaluation criteria, as illustrated in Figure 3. Beyond the criteria listed in Table A, we also use other criteria (security, privacy, research contribution, etc.) to illustrate the hierarchy. As mentioned above and as appears in Figure 3, many of the evaluation criteria appear at the bottom level of the hierarchy (utilitarian criteria). These criteria are inherently associated with the artifact: they qualify its behavior, e.g. functionality, and/or its structure, e.g. decomposability. As we move upwards in the hierarchy, subjectivity plays a greater role, the criteria being more related to the perception of individuals (e.g. style). At the upper level, innovation criteria measure the new knowledge added to the knowledge bases of the application domain and the degree to which the artifact can be generalized to new situations. At the top level, evolution criteria measure the extent to which the artifact is capable of accommodating changes in its context (e.g., malleability) and/or its goals (e.g. learning capability).

DSR Processes for Identifying and Managing Goals and Evaluation Criteria

The iterative DSR project process is composed of three key stages: 1) defining the problem, 2) building a solution, and 3) assessing DSR goals attainment. Figure 4 expands the framework via its interactions in a DSR project with process and information flows. Evaluation criteria link the three steps by providing a means to assess the fitness between problem components (context and goals) and designed components (structures and behaviors) of the solution (the DSR artifact). This framework provides an organization of the DSR project not previously seen in the literature and sheds new light on the richness of artifact construction and evaluation. In this section, we discuss the processes and information found in each of the three dimensions of the framework. Our focus is on the roles of DSR goals and corresponding evaluation criteria throughout the framework. DSR goals address the meaning and requirements for how well a design solution solves the problem in context. Once the goals for the problem are understood, we identify the evaluation criteria that are relevant and capture the essential requirements for a design solution. The explicit steps for identifying a good set of evaluation criteria are left as future research directions. As discussed in the previous section, any 10 practical solution must include evaluation criteria that focus broadly on all six-levels of the goal hierarchy. Thus, evaluation criteria for satisfactory solutions will include a rich mix of measures from the categories of utility, safety, interaction/communication, cognitive/aesthetic, innovation and evolution. We note that a particular DSR project may not include criteria from all six levels but it would be important to consider all the levels for a full understanding of the problem. The description of these evaluation criteria provides a rigorous set of acceptance criteria for the evaluation of potential design solutions and establishes guidance for the design of both formative and summative evaluation methods [START_REF] Venable | FEDS: a Framework for Evaluation in Design Science Research[END_REF].

DSR Solution

A DSR project creates a solution via build and evaluate sub-processes [START_REF] Hevner | Design Science in Information Systems Research[END_REF]). The project produces design artifacts in the form of constructs, models, methods, and instantiations. Artifacts must be complete representations possessing a structure (i.e. form) and a set of behaviors (i.e. functions). Information on context, goals, and evaluation criteria provides essential guidance to both the build and evaluate subprocesses. During construction of solution artifacts, search processes identify the best design candidates. Information on environmental context and evaluation criteria is used to guide a goal-driven search to maximize value while being constrained by the availability and feasibility of resources, including project time deadlines. Evaluation criteria particularly come into play in the design and execution of formative evaluations of the artifacts. Iterative build-evaluate cycles will refine the structure and activities of the design artifacts to best meet the goals.

Assessing DSR Goals

The third step develops the crucial bridge of summative evaluation between the problem and the solution. We look for compelling evidence from these evaluations of the innovative design artifacts to provide confirmation of the success or failure of the DSR project to satisfactorily solve the problem. We note that not all DSR projects have the opportunity to test the new design artifacts in realistic environments. In those cases, opportunities for summative evaluations in artificial environments should be considered (e.g. simulation, predictive analytic modeling) [START_REF] Prat | A Taxonomy of Evaluation Methods for Information Systems Artifacts[END_REF].

DSR Project Flows and Evaluation Criteria

Figure 4 illustrates the flows of process and information in a DSR project. The DSR process flow moves in an iterative cycle from Problem Space to Solution Space to Project Assessment. As the project progresses through multiple iterations of this cycle, a repository of project design knowledge accumulates rapidly. Emerging understanding of the problem produces a detailed description of the environment and a growing set of evaluation criteria. The Solution Space inputs this information and performs iterative artifact design cycles of build and evaluation sub-processes. In turn, the Solution Space produces design knowledge in the form of artifacts with well-defined structures and activities. Then the assessment step evaluates the artifact for goodness of fit to the problem environment and goals. A decision is made on whether the current artifact fit is satisfactory for solution delivery or if additional iterations of the overall DSR project cycle are required to grow needed design knowledge to better solve the problem.

Illustrative Example

To illustrate the proposed DSR process, consider a research context where a thesis supervisor assigns a literature review task to her PhD student. The student must identify all the machine learning papers regarding consumer behaviours in a specific application context. The supervisor suggests building a taxonomy of the different solutions. The goals hierarchy facilitates the supervisor's validation effort. Building the taxonomy forces the PhD student to study deeply the set of papers. This is clearly related to the utilitarian goal. Besides, the taxonomy is delivered with dimensions and characteristics which improve the understandability of the field (cognitive goal) and represent a research contribution (innovation goal). The PhD supervisor must verify that the taxonomy is robust and may survive during the thesis period (evolution goal). This illustrative example is a first step towards a more comprehensive validation, to be developed in our further research.

Conclusion and Further Research

The effectiveness of a Design Science Research (DSR) project is judged both by the fitness of the designed artifact as a solution in the application environment and by the level of new research contributions made to the appropriate knowledge bases. An important and under-studied challenge is how to translate DSR project research goals into discrete and measurable evaluation criteria for use in the DSR project processes. We propose an initial structured approach for articulating DSR goals and then identifying project evaluation criteria for these goals. The DSR goals are organized hierarchically: utilitarian goals, safety goals, interaction and communication goals, cognitive and aesthetic goals, innovation goals, and evolution goals. Goals in a DSR project are identified pragmatically, i.e. by considering the components of the context, coupled with the hierarchy of goals. Based on the identified goals, the associated evaluation criteria are determined and organized along the hierarchy of goals. These criteria measure fitness, i.e. the ability of the artifact to meet its goal. This goal-driven approach provides pragmatic insights for managing a DSR project to a successful conclusion with the achievement of measurable goals.

Future work will refine the hierarchy of DSR goals and associated criteria. First, to refine the hierarchy of goals, we will complement the top-down approach used in this paper (adaptation of a generic hierarchy of goals, namely Maslow's hierarchy) with a bottom-up approach (i.e., an approach starting from goals in actual DSR studies). Second, we will expand our literature survey and investigation into the top two levels of the goal hierarchy -innovation goals and evolution goals. As these are the least understood areas, we hope to propose new approaches for linking innovation and evolution goals to specific evaluation criteria. Recent thinking on the building of design theories for complex systems development will provide insights to our research directions (e.g. [START_REF] Hanseth | Design Theory for Dynamic Complexity in Information Infrastructures: The Case of Building Internet[END_REF][START_REF] Demetis | Crafting Theory to Satisfy the Requirements of System Science[END_REF]. Third, we will provide researchers with more intuitive and detailed guidelines facilitating the identification and management of goals and evaluation criteria. Finally, we will explore different usages of the framework, including how a change in the solution impacts its fitness to the problem. This corresponds to tackling the variability of the artifacts. Although this variability concept has been originally developed in software engineering (software product lines), there is research value for its application to DSR project fitness evaluation.

Figure 1 .

 1 Figure 1. Hierarchy of DSR Goals

Figure 2 .

 2 Figure 2. Knowledge Innovation Matrix (from Gregor and Hevner 2014)

Figure 3 .

 3 Figure 3. Hierarchy of DSR Goals and Evaluation Criteria

Figure 4 .

 4 Figure 4. DSR Process Model with Goals and Evaluation Criteria 4.1 DSR Problem Space DSR projects solve important problems in a defined application domain. A detailed understanding and description of the problem are essential to provide a convincing relevance of the research project. There are two key components that describe a project's problem -the environment (i.e. application context) and the DSR goals for solution acceptance.DSR goals address the meaning and requirements for how well a design solution solves the problem in context. Once the goals for the problem are understood, we identify the evaluation criteria that are relevant and capture the essential requirements for a design solution. The explicit steps for identifying a good set of evaluation criteria are left as future research directions. As discussed in the previous section, any

Appendix

Accuracy

The degree of agreement between outputs of the artifact and the expected outputs (ISO/IEC/IEEE)

Adaptability

The ease with which the artifact can work in environments other than those for which it was specifically designed, or change according to evolutions in environment (ISO/IEC/IEEE) Alignment with business

The congruence of the artifact with the organization and its strategy [START_REF] Henderson | Strategic Alignment: Leveraging Information Technology for Transforming Organizations[END_REF]

Completeness

The degree to which the artifact contains all necessary elements and relationships between elements

Consistency

The degree of uniformity, standardization, and freedom from contradiction among the elements of the artifact (ISO/IEC/IEEE)

Ease of use The degree to which the use of the artifact is effort free [START_REF] Davis | Perceived Usefulness, Perceived Ease of Use, and User Acceptance of Information Technology[END_REF] Efficacy

The degree to which the artifact achieves its goal considered narrowly, without addressing situational concerns (Checkland and Scholes 1990; Venable et al.

2016) Ethicality

The degree to which the artifact complies with ethics

Functionality

The capability of the artifact to provide functions which meet stated and implied needs when the artifact is used under specified conditions (ISO/IEC/IEEE) Learning capability

The ability of the artifact to learn from experience

Modifiability

The ease with which the artifact can be changed without introducing defects (ISO/IEC/IEEE)

Performance

The degree to which the artifact accomplishes its function with given constraints of resources (ISO/IEC/IEEE; Glinz 2007)

Robustness

The ability of the artifact to handle invalid inputs or stressful environmental conditions (ISO/IEC/IEEE)

Scalability

The ability of the artifact to handle growing amounts of work in a graceful manner, or to be readily enlarged [START_REF] Williams | Design of Emerging Digital Services: a Taxonomy[END_REF][START_REF] Bondi | Characteristics of Scalability and their Impact on Performance[END_REF] Simplicity

The degree to which the artifact contains the minimal number of elements and relationships between elements (ISO/IEC/IEEE)

Style

The elegance with which the artifact has been built [START_REF] March | Design and Natural Science Research on Information Technology[END_REF][START_REF] Hevner | Design Science in Information Systems Research[END_REF])

Understandability

The degree to which the artifact can be comprehended, both at a global level and at the detailed level of the elements and relationships inside the artifact (ISO/IEC/IEEE) Usefulness

The degree to which the artifact positively impacts the

Applicability

The ease with which the artifact can achieve other goals than the one for which it was specifically designed, or change according to evolutions in goal

Innovativeness

Requires "inventive leaps of generative reasoning" which facilitates trial and error, crucial to creative resolution" [START_REF] Martin | The Opposable Mind: Winning Through Integrative Thinking[END_REF] Inventiveness "The inventiveness of the designer lies in a natural or cultivated and artful ability to return to those placements and apply them to a new situation, discovering aspects of the situation that affect the final design" (Buchanan 1992) Gill and Hevner (2013)

Decomposability

The degree to which the artifact can be disassembled into nearly independent sub-artifacts Embeddedness in a design system

The degree to which the artifact is the product of a sustainable design system environment

Openness

The degree to which the artifact lends itself to inspection [START_REF] Sauser | Systomics: Toward a Biology of System of Systems[END_REF] Diversity

The degree to which the artifact is composed of differing elements