Papers in Physics, vol. 14, art. 140007 (2022) Received: 13 January 2022, Accepted: 11 March 2022 Edited by: K. Daniels, L. A. Pugnaloni, J. Zhao Reviewed by: R. Stannarius - Otto von Guericke Univ. Magdeburg, Germany Licence: Creative Commons Attribution 4.0 DOI: http://doi.org/10.4279/PIP.140007 www.papersinphysics.org ISSN 1852-4249 Bespoke particle shapes in granular matter D. Cantor1∗, M. Cárdenas-Barrantes2,3 †, L. Orozco4 ‡ Among granular matter, one type of particle has special properties. Upon being assembled in disordered configurations, these particles interlock, hook, almost braid, and – surpris- ingly, considering their relatively low packing fractions – show exceptional shear strength. Such is the case of non-convex particles. They have been used in the shapes of tetrapods, ‘L’, ‘Z’, stars, and many others, to protect coasts or build self-standing structures requir- ing no binders or external supports. Although these structures are often designed without a comprehensive mechanical characterization, they have already demonstrated great po- tential as highly resistant construction materials. Nevertheless, it is natural to attempt to find the most appropriate non-convex shapes for any given application. Can a particle shape be tuned to obtain a desired mechanical behavior? Although this question cannot be answered yet, current technological, simulation, and experimental developments strongly suggest that it can be resolved in the next decade. A clear understanding of the relation- ships between particle shapes, mechanical response, and packing properties will be key to providing insights into the behavior of these materials. Such work should stand on 1) ro- bust and general shape descriptors that encode the complexity of non-convex shapes (i.e., the number of arms, the symmetries and asymmetries of the bodies, the presence of holes, etc.), 2) the analysis of the response of assemblies under different loading conditions, and 3) the disposition and reliability of non-convex shapes to ensure durability. The manufac- turing process and an efficient use of resources are additional elements that could further help to optimize particle shape. In the quest of designing bespoke non-convex particles, this paper consolidates the challenges that remain unresolved. It also outlines some routes to explore based on the latest developments in technology and research. ∗ david.cantor@polymtl.ca † manuel-antonio.cardenas-barrantes@umontpellier.fr ‡ l.orozco@uliege.be 1 Department of Civil, Geological and Mining Engineering, Polytechnique Montreal, Montreal, QC, Canada. 2 LMGC, CNRS, University of Montpellier, France. 3 Laboratoire de Micromcanique et Intgrit des Structures (MIST), UM, CNRS, IRSN, France. 4 GRASP, CESAM Research Unit Institute of Physics B5a, University of Lige, Belgium. I. Introduction Have you observed tetrapod-like elements protect- ing coasts? Or, perhaps, an assembly of rigid stars collectively building a structure? Figure 1 shows complex arrangements of interlocked non-convex particles forming relatively loose structures with remarkable strength and dissipative properties. In many places around the world, concrete non-convex blocks are used for coastal protection due to their easy prefabrication and disposition methods [1–4] (see Fig. 1(a)). These blocks create stable, loose configurations that allow water to enter the cavities and, thus, release the kinetic energy of the waves. 140007-1 Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. Figure 1(b) shows a self-standing structure eas- ily reaching a few meters high, requiring no exter- nal support or binding materials. These innova- tive applications expose the great potential non- convex particles possess as construction materi- als where interlocking, braiding, or stacking ele- ments can dramatically improve mechanical prop- erties [5–11]. In addition, non-convex shapes such as ‘Z’ [11] can also continuously gain shear strength as strains do not necessarily trigger failure, but rather promote particle rearrangement and further interlocking [12–14]. Since the particles used for many of these applications are replicated from a single shape – or a few shapes –, the fabrication processes and disposition of the pieces can be au- tomated for construction in environments of diffi- cult access or that require remote-controlled ma- chinery/robots [15, 16]. It is evident that non-convex particles could vary infinitely in shape. In practice, there are branched, twisted, curved, asymmetric, and even convex shapes with hollowed faces creating truss structures [17–19]. It is natural, then, to inquire into the best shape for a given application. Although intuition may suggest that assemblies of ‘Z’ or ‘L’ shaped parti- cles can develop higher strengths, there are no sys- tematic studies allowing one to determine which non-convex shape performs better than another. So far, studies have used different particle shapes and tested various characterization approaches that produce no comparable results. While the particle shape is central to designing tailored/bespoke gran- ular materials, other aspects such as deposition or assembly methods, particle strength, and construc- tive processes should also be considered to optimize the particle geometry for a given application. In the following, we present the challenges that, in our opinion, can be addressed in the near future to make bespoke granular matter the next genera- tion of construction materials. II. Challenges i. How is particle geometry described? Many shape descriptors found in the literature are focused on describing convex shapes (i.e., shapes without cavities) by means of their sphericity, as- pect ratio, angularity, flatness, elongation, round- ness, and irregularity [22–28]. These parameters often fail to describe the complexity of non-convex shapes or do not allow one to have a straightforward picture of the particle. As an alternative, Fourier descriptors have been used to represent non-convex shapes [29, 30]. However, this method may need a large set of parameters when dealing with asym- metric or highly irregular geometries. In general, there is no consensus on a parameter or a set of pa- rameters to describe the complexity of non-convex bodies. The first challenge is the development of simple and robust geometrical descriptors, allowing one to compare different families of particle shapes. This descriptor - or set of descriptors - should be able to encode as much information as possible regard- ing the characteristics of non-convex shapes, such as the number of arms, symmetry or asymmetry of the body, the presence of holes, recurrent pat- terns, among others. Furthermore, any descriptor should be sufficiently clearsuch that its definition maps directly into basic or elemental parameters. Once the descriptors are set, efforts should be focused on systematically linking them to the me- chanical behavior (compaction, shear strength, rhe- ology of quasi-static and inertial flows) and pack- ing properties of particle assemblies. For this, ex- periments and simulations are valuable tools that should be developed to work in synergy and mutu- ally enrich each other’s observations. ii. Physical experiments In experiments, for example, the technology of 3D printing has allowed one to precisely control the shape of particles to be later assembled in struc- tures [31]. Although some studies have performed qualitative characterization of the resistance of non-convex particle assemblies [5, 9, 10, 32], only a few have quantitatively assessed their mechanical response and packing properties [11, 33–36]. The current technological capabilities suggest that hun- dreds - or even thousands - of particles can be built and tested in standard devices (triaxial, shear cells, rheometers, etc.). However, to the best of our knowledge, this has not been done. Besides, it is unclear how to scale up the obtained properties from the laboratory scale to large size applications such as coastal barriers. The second challenge is related to the fabrication 140007-2 Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. (a) (b) Figure 1: Examples of structures built using non-convex particles: a) coastal barrier (public image by Pok Rie [20]) and b) aggregate wall (with permission of Karola Dierichts [21]). of non-convex shapes and the mechanical character- ization of assemblies either in standard equipment or non-conventional devices (e.g., large-scale shear boxes [37, 38]). Up to now, the physical characterization we have mentioned refers to macroscopic mechanical or packing properties. However, it is well known that such responses are related to the mechanics at the scale of the particles and their contacts [39–41]. Recently, several efforts have been put into charac- terizing the mechanics at such small scales. For in- stance, novel fast digital image analysis allows one to track a particle’s positions when loaded [42–45]. Among them, it is worth mentioning the use of photo-elastic particles, which can not only display the contact network, but also permits us to esti- mate the force and stress intensities within the par- ticles [46–49]. Despite the advances in these experimental ap- proaches, their use is seldom seen when it comes to non-convex particle assemblies. The third challenge corresponds to exploring the microstructure and force transmission mechanisms within assemblies of non-convex bodies. This re- quires the development of robust and efficient digi- tal image analyses capable of dealing with complex entangled particles that are often ambiguous, diffi- cult to identify one from another. iii. Numerical simulations An alternative means to probe the packing proper- ties and load distribution within a granular sample is numerical simulations. To simulate discrete mat- ter, some of the most popular approaches are the discrete-element method (DEM) [50–52], and the material point method (MPM) [53–55]. In particu- lar, DEM strategies have proven to be quite advan- tageous since they provide a detailed description of the micromechanics of granular materials (e.g., par- ticle connectivity, fabric anisotropy, contact force network, etc.) while being capable of dealing with collections of rigid [56, 57] and deformable bodies [58–60] of varied sizes and shapes [61, 62], under a large variety of boundary conditions. Even though the simulation of non-convex gran- ular assemblies is in rapid development today [17, 63–70], these works also expose some of the limita- tions of the current modeling approaches. First, the shape of the bodies is sometimes represented using clumped spheres [71], sphero-polyhedra [72, 73] or superquadrics [74]. Although these strategies allow one to use well-known methods for convex bodies, the discretization of the shapes may add artificial textures on the surfaces, or they can be rapidly lim- ited when pointy geometries or sharp edges need to be considered. Other strategies that discretize bod- ies using multiple vertices and faces to represent the particles often require excessive storage space and expensive I/O operations that penalize the num- 140007-3 Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. ber of particles that can be considered. Secondly, contact detection strategies require further opti- mization and are computationally prohibitive when dealing, for instance, with elongated or long-armed bodies. Since contact detection is often based on the overlapping of spheres enveloping the bodies, such approaches can largely overestimate potential contacts in the case of non-convex particles, which can dramatically slow down the time stepping evo- lution of a simulation. Finally, it remains difficult to draw clear comparisons between studies given the broad spectrum of particle shapes considered and the lack of a consensus, once again, in the pa- rameters to describe non-convex geometries. The fourth challenge is to develop new algo- rithms that provide an accurate representation of non-convex shapes while facilitating or optimizing contact detection. These developments should be conceived and developed as scalable, highly parallel algorithms that could be used in cluster comput- ing (e.g., HPC and GPU computing). Equally im- portant will be validating the well-known microme- chanical analyses of granular materials to any par- ticle shape by means of simulation campaigns over a broad range of parameters. The advances on the experimental and simula- tion axes will naturally lead to the validation of the numerical models that, then, can be extended to more complex particle shapes and boundary con- ditions. Extensive systematic simulation studies, in which one can clearly control the physical and numerical parameters, can thus provide further in- sights into the mechanical behavior of granular matter composed of non-convex bodies. III. Tuning particle shape for appli- cations While theoretical, experimental, and numerical ap- proaches are valuable tools to explore the mechan- ics of granular media, the applications or indus- trial stakes may determine pertinent features that particles and assemblies should exhibit. As men- tioned before, coastal protection structures have consisted of various shapes, including tetrapods, tripods, cubes, dolossa, etc. Even though all of them dissipate energy and contribute to erosion prevention, it is not clear which features led en- gineers to prefer one shape over others. The fifth challenge is to develop methodologies to tune particle shape for a specific application, based on the thorough geometrical and mechanical char- acterization of non-convex shapes. Although the mechanical response of the granu- lar assemblies can often be the key parameter to choose a specific particle shape, other elements ac- counting for the durability and reliability of the structures should also be considered. For in- stance, additional analyses may include the break- age strength of the particles, the settlements over time due to particle rearrangement, the capabili- ties for particle manufacturing, and the initial con- ditions of the arrangements (e.g., deposition, pre- loading, etc.). More recently, the scarcity of materials due to supply chain unreliability and the need for reduc- ing ecological footprints are issues that call for the reusability of the individual bodies, or for their be- ing manufactured from local materials. This last challenge is indeed broader and may involve the science of new composite materials from renewable sources. Nevertheless, the task may largely benefit from advances in the mechanics of granular media of varied shaped bodies. IV. Summary and perspectives Arrangements of non-convex particles often present outstanding properties regarding their shear strength, mainly due to their capacity to hook, in- terlock, and entangle. These materials also present low packing fractions which favor efficient energy dissipation, as in the case of coastal barriers. De- spite the multiple advantages non-convex particle assemblies can display, their mechanical behavior is still poorly understood. Indeed, there are no methodologies to determine what shapes provide more strength than others, and it is not clear how to optimize particle shape for a given application. To correctly match non-convex particle shapes to applications, a series of challenges need to be over- come. They include 1) the development of robust - yet simple - geometrical descriptors, allowing one to compare different shapes; 2) the generation of par- ticle assemblies for systematic studies on their me- chanical properties with experiments and numeri- cal simulations. The synergy between experiments and numerical modeling will be key to rapidly gath- 140007-4 Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. ering insights on the mechanical behavior of these materials; 3) the micro-mechanical analyses to un- derstand the particularities of these materials that lead to their exceptional macroscopical properties; and finally, 4) the identification of additional ele- ments that limit the range of possibilities for parti- cle shape or allow one to optimize the mechanical properties for a given application. State-of-the-art experiments and simulations suggest that these challenges can be successfully addressed in the near future. In terms of experi- ments, X-ray tomography, 3D printing, and digital image analyses are promising tools and strategies largely used for convex grains, awaiting general- ization to any particle shape. Regarding numeri- cal modeling, discrete-element approaches seem to present a privileged framework for exploring the macro and microscopic responses of assemblies of complex shaped bodies. However, this task requires several improvements in the algorithms’ efficiency and their scalability to work on highly parallelized environments. Although artificial intelligence (AI) is just debuting in the field of granular materials [75, 76], it is going to be an essential tool for the optimization of particle shapes under a set of con- straints. These AI tools will benefit from the ex- perimental and numerical axes of research and can shed light into more fundamental aspects concern- ing a unified geometrical descriptor for non-convex grains and the physics of granular media. Optimizing particle shapes in granular matter will also benefit from multidisciplinary contribu- tions including mathematics, statistics, computer science, chemistry, among others. Although we focused our exposition on civil structures, this is a topic spanning different fields of material tech- nology, engineering, architecture, bio-inspired ma- terials, etc. Undoubtedly, materials composed of non-convex particles may be the next generation of building materials for optimized structures based on the idea of tailored granular matter or bespoke particle shapes. Acknowledgements - The authors would like to acknowledge fruitful discussion with Jonathan Barés and Emilien Azéma. [1] P Danel, Tetrapods, Coast. Eng. Proc. 1, 28 (1953). [2] M Muttray, B Reedijk, Design of concrete ar- mour layers, Hansa Int. Maritime J. 6, 111 (2009). [3] J R Medina, J Molines, M E Gómez-Mart́ın, Influence of armour porosity on the hydraulic stability of cube armour layers, Ocean Eng. 88, 289 (2014). [4] J Molines, R Centi, M Di Risio, J R Med- ina, Estimation of layer coefficients of cubi- pod homogeneous low-crested structures using physical and numerical model placement tests, Coast. Eng. 168, 103901 (2021). [5] O Tessmann, Topological interlocking assem- blies, Proc. 30th Int. Conf. eCAADe 2, 201 (2012). [6] S V Franklin, Geometric cohesion in granular materials, Phys. Today 65, 70 (2012). [7] N Gravish, S V Franklin, D L Hu, D I Gold- man, Entangled granular media, Phys. Rev. Lett. 108, 208001 (2012). [8] K Dierichs, A Menges, Aggregate architecture: Simulation models for synthetic non-convex granulates, Proc. 33rd Annual Conf. ACADIA, 301 (2013). [9] K Dierichs, A Menges, Towards an aggregate architecture: Designed granular systems as programmable matter in architecture, Granul. Matter 18, 1 (2016). [10] Y Zhao, K Liu, M Zheng, J Barés, K Dierichs, A Menges, R Behringer, Packings of 3D stars: Stability and structure, Granul. Matter 18, 1 (2016). [11] K A Murphy, N Reiser, D Choksy, C E Singer, H M Jaeger, Freestanding loadbearing struc- tures with Z-shaped particles, Granul. Matter 18, 1 (2016). [12] D Dumont, M Houze, P Rambach, T Salez, S Patinet, P Damman, Emergent strain stiff- ening in interlocked granular chains, Phys. Rev. Lett. 120, 088001 (2018). 140007-5 https://doi.org/10.9753/icce.v4.28 https://doi.org/10.9753/icce.v4.28 https://www.researchgate.net/profile/Bas-Reedijk/publication/275960407_Design_of_Concrete_Armour_Layers/links/554b8c450cf21ed213594b1a/Design-of-Concrete-Armour-Layers.pdf https://www.researchgate.net/profile/Bas-Reedijk/publication/275960407_Design_of_Concrete_Armour_Layers/links/554b8c450cf21ed213594b1a/Design-of-Concrete-Armour-Layers.pdf https://doi.org/10.1016/j.oceaneng.2014.06.012 https://doi.org/10.1016/j.oceaneng.2014.06.012 https://doi.org/10.1016/j.coastaleng.2021.103901 http://papers.cumincad.org/data/works/att/ecaade2012_176.content.pdf http://papers.cumincad.org/data/works/att/ecaade2012_176.content.pdf https://doi.org/10.1063/PT.3.1726 https://doi.org/10.1103/PhysRevLett.108.208001 https://doi.org/10.1103/PhysRevLett.108.208001 http://papers.cumincad.org/data/works/att/acadia13_301.content.pdf http://papers.cumincad.org/data/works/att/acadia13_301.content.pdf https://doi.org/10.1007/s10035-016-0631-3 https://doi.org/10.1007/s10035-016-0631-3 https://doi.org/10.1007/s10035-016-0606-4 https://doi.org/10.1007/s10035-016-0606-4 https://doi.org/10.1007/s10035-015-0600-2 https://doi.org/10.1007/s10035-015-0600-2 https://doi.org/10.1103/PhysRevLett.120.088001 https://doi.org/10.1103/PhysRevLett.120.088001 Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. [13] A Hafez, Q Liu, T Finkbeiner, R A Alouhali, T E Moellendick, J C Santamarina, The ef- fect of particle shape on discharge and clogging, Sci. Rep. 11, 1 (2021). [14] Y Zhao, J Barés, J E S Socolar, Yielding, rigidity, and tensile stress in sheared columns of hexapod granules, Phys. Rev. E 101, 062903 (2020). [15] K Dierichs, O Kyjánek, M Loučka, A Menges, Construction robotics for designed granular materials: In situ construction with designed granular materials at full architectural scale using a cable-driven parallel robot, Constr. Robotics 3, 41 (2019). [16] E P G Bruun, R Pastrana, V Paris, A Begh- ini, A Pizzigoni, S Parascho, S Adriaenssens, Three cooperative robotic fabrication methods for the scaffold-free construction of a masonry arch, Autom. Constr. 129, 103803 (2021). [17] A G Athanassiadis, M Z Miskin, P Kaplan, N Rodenberg, S H Lee, J Merritt, E Brown, J Amend, H Lipson, H M Jaeger, Particle shape effects on the stress response of granular packings, Soft Matter 10, 48 (2014). [18] C Avendao, F A Escobedo, Packing, entropic patchiness, and self-assembly of non-convex colloidal particles: A simulation perspective, Curr. Opin. Colloid In. 30, 62 (2017). [19] Y Wang, L Li, D Hofmann, J E Andrade, C Daraio, Structured fabrics with tunable me- chanical properties, Nature 596, 238 (2021). [20] Aerial view of breakwater, Pok Rie, Marang, Malaysia. [21] ICD Aggregate Wall 2017, Institute for Com- putational Design and Construction (ICD), University of Stuttgart (2017). [22] Hakon Wadell, Volume, shape, and roundness of rock particles, J. Geol. 40, 443 (1932). [23] W C Krumbein, Measurement and geological significance of shape and roundness of sedi- mentary particles, J. Sediment. Res. 11, 64 (1941). [24] G Lees, A new method for determining the angularity of particles, Sedimentology 3, 2 (1964). [25] S J Blott, K Pye, Particle shape: A review and new methods of characterization and clas- sification, Sedimentology 55, 31 (2008). [26] C R I Clayton, C O R Abbireddy, R Schiebel, A method of estimating the form of coarse par- ticulates, Géotechnique 59, 493 (2009). [27] G H Bagheri, C Bonadonna, I Manzella, P Vonlanthen, On the characterization of size and shape of irregular particles. Powder Tech- nol. 270 A, 141 (2015). [28] M A Maroof, A Mahboubi, A Noorzad, Yaser Safi, A new approach to particle shape classifi- cation of granular materials, Transp. Geotech. 22, 100296 (2020). [29] E T Bowman, K Soga, W Drummond, Particle shape characterisation using Fourier descrip- tor analysis, Géotechnique 51, 545 (2001). [30] G Mollon, J Zhao, 3D generation of realistic granular samples based on random fields the- ory and Fourier shape descriptors, Comput. Method. Appl. Mech. Eng. 279, 46 (2014). [31] D A H Hanaor, Y Gan, M Revay, D W Airey, I Einav, 3D printable geomaterials, Gotech- nique 66, 323 (2016). [32] H Zheng, D Wang, J Barés, R Behringer, Jamming by compressing a system of granular crosses, EPJ Web Conf. 140, 06014 (2017). [33] D P Huet, M Jalaal, R van Beek, D van der Meer, A Wachs, Granular avalanches of en- tangled rigid particles, Phys. Rev. Fluids 6, 104304 (2021). [34] J Landauer, M Kuhn, D S Nasato, P Fo- erst, H Briesen, Particle shape matters - Using 3D printed particles to investigate fundamental particle and packing properties, Powder Tech- nol. 361, 711 (2020). [35] N Weiner, Y Bhosale, M Gazzola, H King, Mechanics of randomly packed filaments - The ”bird nest” as meta-material, J. Appl. Phys. 127, 050902 (2020). 140007-6 https://doi.org/10.1038/s41598-021-82744-w https://doi.org/10.1103/PhysRevE.101.062903 https://doi.org/10.1103/PhysRevE.101.062903 https://doi.org/10.1007/s41693-019-00024-6 https://doi.org/10.1007/s41693-019-00024-6 https://doi.org/10.1016/j.autcon.2021.103803 https://doi.org/10.1039/C3SM52047A https://doi.org/10.1016/j.cocis.2017.05.005 https://doi.org/10.1038/s41586-021-03698-7 https://www.pexels.com/photo/aerial-view-of-breakwater-with-concrete-dolosse-5854657/ https://www.pexels.com/photo/aerial-view-of-breakwater-with-concrete-dolosse-5854657/ https://www.icd.uni-stuttgart.de/projects/icd-aggregate-wall-2017/ https://www.icd.uni-stuttgart.de/projects/icd-aggregate-wall-2017/ https://www.icd.uni-stuttgart.de/projects/icd-aggregate-wall-2017/ https://doi.org/10.1086/623964 https://doi.org/10.1306/D42690F3-2B26-11D7-8648000102C1865D https://doi.org/10.1306/D42690F3-2B26-11D7-8648000102C1865D https://doi.org/10.1111/j.1365-3091.1964.tb00271.x https://doi.org/10.1111/j.1365-3091.1964.tb00271.x https://doi.org/10.1111/j.1365-3091.2007.00892.x https://doi.org/10.1680/geot.2007.00195 https://doi.org/10.1016/j.powtec.2014.10.015 https://doi.org/10.1016/j.powtec.2014.10.015 https://doi.org/10.1016/j.trgeo.2019.100296 https://doi.org/10.1016/j.trgeo.2019.100296 https://doi.org/10.1680/geot.2001.51.6.545 https://doi.org/10.1016/j.cma.2014.06.022 https://doi.org/10.1016/j.cma.2014.06.022 https://doi.org/10.1680/jgeot.15.P.034 https://doi.org/10.1680/jgeot.15.P.034 https://doi.org/10.1051/epjconf/201714006014 https://doi.org/10.1103/PhysRevFluids.6.104304 https://doi.org/10.1103/PhysRevFluids.6.104304 https://doi.org/10.1016/j.powtec.2019.11.051 https://doi.org/10.1016/j.powtec.2019.11.051 https://doi.org/10.1063/1.5132809 https://doi.org/10.1063/1.5132809 Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. [36] R Stannarius, J Schulze, On regular and random two-dimensional packing of crosses, Granul. Matter 24, 25 (2022). [37] C Ovalle, E Frossard, C Dano, W Hu, S Maiolino, P-Y Hicher, The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data, Acta Mech. 225, 2199 (2014). [38] S Linero-Molina, L Bradfield, S G Fityus, J V Simmons, A Lizcano, Design of a 720-mm square direct shear box and investigation of the impact of boundary conditions on large-scale measured strength, Geotech. Test. J. 43, 1463 (2020). [39] L Rothenburg, R J Bathurst, Analytical study of induced anisotropy in idealized granular ma- terial, Géotechnique 39, 601 (1989). [40] B Andreotti, Y Forterre, O Pouliquen, Granu- lar media: Between fluid and solid, Cambridge University Press, New York (2013). [41] J C Santamarina, G C Cho, Soil behaviour: The role of particle shape, Proc. Adv. Geotech. Eng.: The Skempton Conference , 604 (2004). [42] E Andò, S A Hall, G Viggiani, J Desrues, P Bésuelle, Grain-scale experimental investiga- tion of localised deformation in sand: A dis- crete particle tracking approach, Acta Geotech. 7, 1 (2012). [43] C R K Windows-Yule, T Weinhart, D J Parker, A R Thornton, Effects of packing den- sity on the segregative behaviors of granular systems, Phys. Rev. Lett. 112, 098001 (2014). [44] E E Ehrichs, H M Jaeger, G S Karczmar, J B Knight, V Y Kuperman, S R Nagel, Granu- lar convection observed by magnetic resonance imaging, Science 267, 1632 (1995). [45] S S Shirsath, J T Padding, H J H Clercx, J A M Kuipers, Cross-validation of 3D particle tracking velocimetry for the study of granular flows down rotating chutes, Chem. Eng. Sci. 134, 312 (2015). [46] D Muir Wood, D Leśniewska, Stresses in gran- ular materials, Granul. Matter 13, 395 (2011). [47] R Hurley, E Marteau, G Ravichandran, José E Andrade, Extracting inter-particle forces in opaque granular materials: Beyond photoelas- ticity, J Mech. Phys. Solids 63, 154 (2014). [48] K E Daniels, J E Kollmer, J G Puckett, Pho- toelastic force measurements in granular ma- terials, Rev. Sci. Instrum. 88, 051808 (2017). [49] A A Zadeh, J Barés, T A Brzinski, K E Daniels, et al, Enlightening force chains: A review of photoelasticimetry in granular mat- ter, Granul. Matter 21, 1 (2019). [50] P A Cundall, O D L Strack, A dis- crete numerical model for granular assemblies, Géotechnique 29, 47 (1979). [51] M Jean, J-J Moreau, Unilaterality and dry friction in the dynamics of rigid body collec- tions, Proc. 1st. Contact Mech. Int. Symp., 31 (1992). [52] F Dubois, V Acary, M Jean, The Contact Dy- namics method: A nonsmooth story, C. R. Mécanique 346, 247 (2018). [53] D Sulsky, Z Chen, H L Schreyer, A par- ticle method for history-dependent materials, Comput. Method. Appl. Mech. Eng. 118, 179 (1994). [54] S G Bardenhagen, J U Brackbill, D Sulsky, The material-point method for granular ma- terials, Comput. Method. Appl. Mech. Eng. 187, 529 (2000). [55] K Soga, E Alonso, A Yerro, K Kumar, S Ban- dara, Trends in large-deformation analysis of landslide mass movements with particular em- phasis on the material point method, Gotech- nique 66, 248 (2016). [56] L F Orozco, J-Y Delenne, P Sornay, F Rad- jai, Rheology and scaling behavior of cascading granular flows in rotating drums, J. Rheol. 64, 915 (2020). [57] Y Huillca, M Silva, C Ovalle, J C Quezada, S Carrasco, G E Villavicencio, Modelling size effect on rock aggregates strength using a DEM bonded-cell model, Acta Geotech. 16, 699 (2021). 140007-7 https://doi.org/10.1007/s10035-021-01190-7 https://doi.org/10.1007/s00707-014-1127-z https://doi.org/10.1520/GTJ20190344 https://doi.org/10.1520/GTJ20190344 https://doi.org/10.1680/geot.1989.39.4.601 https://www.cambridge.org/9781107034792 https://www.cambridge.org/9781107034792 https://www.icevirtuallibrary.com/doi/abs/10.1680/aigev1.32644.0035 https://www.icevirtuallibrary.com/doi/abs/10.1680/aigev1.32644.0035 https://doi.org/10.1007/s11440-011-0151-6 https://doi.org/10.1007/s11440-011-0151-6 https://doi.org/10.1103/PhysRevLett.112.098001 https://doi.org/10.1126/science.267.5204.1632 https://doi.org/10.1016/j.ces.2015.05.005 https://doi.org/10.1016/j.ces.2015.05.005 https://doi.org/10.1007/s10035-010-0237-0 https://doi.org/10.1016/j.jmps.2013.09.013 https://doi.org/10.1063/1.4983049 https://doi.org/10.1007/s10035-019-0942-2 https://doi.org/10.1680/geot.1979.29.1.47 https://hal.archives-ouvertes.fr/hal-01863710 https://hal.archives-ouvertes.fr/hal-01863710 https://doi.org/10.1016/j.crme.2017.12.009 https://doi.org/10.1016/j.crme.2017.12.009 https://doi.org/10.1016/0045-7825(94)90112-0 https://doi.org/10.1016/0045-7825(94)90112-0 https://doi.org/10.1016/S0045-7825(99)00338-2 https://doi.org/10.1016/S0045-7825(99)00338-2 https://doi.org/10.1680/jgeot.15.LM.005 https://doi.org/10.1680/jgeot.15.LM.005 https://doi.org/10.1122/1.5143023 https://doi.org/10.1122/1.5143023 https://doi.org/10.1007/s11440-020-01054-z https://doi.org/10.1007/s11440-020-01054-z Papers in Physics, vol. 14, art. 140007 (2022) / D. Cantor et al. [58] T-L Vu, J Barés, S Mora, S Nezamabadi, Nu- merical simulations of the compaction of as- semblies of rubberlike particles: A quantita- tive comparison with experiments, Phys. Rev. E 99, 062903 (2019). [59] D Cantor, M Cárdenas-Barrantes, I Preechawuttipong, M Renouf, E Azéma, Compaction model for highly deformable particle assemblies, Phys. Rev. Lett. 124, 208003 (2020). [60] M Cárdenas-Barrantes, D Cantor, J Barés, M Renouf, Emilien Azéma, Three-dimensional compaction of soft granular packings, Soft Matter 18, 312 (2022). [61] C Voivret, F Radjäı, J-Y Delenne, M S El Youssoufi, Multiscale force networks in highly polydisperse granular media, Phys. Rev. Lett. 102, 178001 (2009). [62] D Cantor, E Azéma, I Preechawuttipong, Mi- crostructural analysis of sheared polydisperse polyhedral grains, Phys. Rev. E 101, 062901 (2020). [63] A D Rakotonirina, J-Y Delenne, F Radjai, A Wachs, Grains3D, a flexible DEM approach for particles of arbitrary convex shape Part III: Extension to non-convex particles mod- elled as glued convex particles, Comp. Part. Mech. 6, 55 (2019). [64] I Malinouskaya, V V Mourzenko, J-F Thovert, P M Adler, Random packings of spiky parti- cles: Geometry and transport properties, Phys. Rev. E 80, 011304 (2009). [65] L Meng, X Yao, X Zhang, Two-dimensional densely ordered packings of non-convex bend- ing and assembled rods, Particuology 50, 35 (2020). [66] F Ludewig, N Vandewalle, Strong interlock- ing of nonconvex particles in random packings, Phys. Rev. E 85, 051307 (2012). [67] E Azéma, F Radjäı, B Saint-Cyr, J-Y De- lenne, P Sornay, Rheology of three-dimensional packings of aggregates: Microstructure and ef- fects of nonconvexity, Phys. Rev. E 87, 052205 (2013). [68] J-P Latham, J Mindel, J Xiang, R Guises, X Garcia, C Pain, G Gorman, M Piggott, A Munjiza, Coupled FEMDEM/Fluids for coastal engineers with special reference to ar- mour stability and breakage, Geomech Geoen- gin. 4, 39 (2009). [69] C F Schreck, N Xu, C S O’Hern, A comparison of jamming behavior in systems composed of dimer- and ellipse-shaped particles, Soft Mat- ter 6, 2960 (2010). [70] T A Marschall, S Teitel, Athermal shearing of frictionless cross-shaped particles of varying aspect ratio, Granul. Matter 22, 1 (2020). [71] N A Conzelmann, A Penn, M N Partl, F J Clemens, L D Poulikakos, C R Müller, Link be- tween packing morphology and the distribution of contact forces and stresses in packings of highly nonconvex particles, Phys. Rev. E 102, 062902 (2020). [72] F Alonso-Marroqúın, Spheropolygons: A new method to simulate conservative and dissipa- tive interactions between 2D complex-shaped rigid bodies, Europhys. Lett. 83, 14001 (2008). [73] S Zhao, J Zhao, A poly-superellipsoid-based ap- proach on particle morphology for DEM mod- eling of granular media, Int. J. Numer. Anal. Meth. Geomech. 43, 2147 (2019). [74] S Wang, D Marmysh, S Ji, Construction of ir- regular particles with superquadric equation in DEM, Theor. App. Mech. Lett. 10, 68 (2020). [75] Z Cheng, J Wang, Estimation of contact forces of granular materials under uniaxial com- pression based on a machine learning model, Granul. Matter 24, 17 (2022). [76] G Ma, J Mei, K Gao, J Zhao, W Zhou, D Wang, Machine learning bridges microslips and slip avalanches of sheared granular gouges, Earth Planet. Sc. Lett. 579, 117366 (2022). 140007-8 https://doi.org/10.1103/PhysRevE.99.062903 https://doi.org/10.1103/PhysRevE.99.062903 https://doi.org/10.1103/PhysRevLett.124.208003 https://doi.org/10.1103/PhysRevLett.124.208003 https://doi.org/10.1039/D1SM01241J https://doi.org/10.1039/D1SM01241J https://doi.org/10.1103/PhysRevLett.102.178001 https://doi.org/10.1103/PhysRevLett.102.178001 https://doi.org/10.1103/PhysRevE.101.062901 https://doi.org/10.1103/PhysRevE.101.062901 https://doi.org/10.1007/s40571-018-0198-3 https://doi.org/10.1007/s40571-018-0198-3 https://doi.org/10.1103/PhysRevE.80.011304 https://doi.org/10.1103/PhysRevE.80.011304 https://doi.org/10.1016/j.partic.2019.05.003 https://doi.org/10.1016/j.partic.2019.05.003 https://doi.org/10.1103/PhysRevE.85.051307 https://doi.org/10.1103/PhysRevE.87.052205 https://doi.org/10.1103/PhysRevE.87.052205 https://doi.org/10.1080/17486020902767362 https://doi.org/10.1080/17486020902767362 https://doi.org/10.1039/C001085E https://doi.org/10.1039/C001085E https://doi.org/10.1007/s10035-019-0966-7 https://doi.org/10.1103/PhysRevE.102.062902 https://doi.org/10.1103/PhysRevE.102.062902 https://doi.org/10.1209/0295-5075/83/14001 https://doi.org/10.1002/nag.2951 https://doi.org/10.1002/nag.2951 https://doi.org/10.1016/j.taml.2020.01.021 https://doi.org/10.1007/s10035-021-01160-z https://doi.org/10.1016/j.epsl.2022.117366 Introduction Challenges How is particle geometry described? Physical experiments Numerical simulations Tuning particle shape for applications Summary and perspectives