Evolving design rules for the inverse granular packing problem

Abstract

If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a solution to this inverse-packing problem by framing it in the context of artificial evolution. By representing shapes as bonded spheres, we show how shapes may be mutated, simulated, and selected to produce particularly dense or loose packing aggregates, both with and without friction. Moreover, we show how motifs emerge linking these shapes together. The result is a set of design rules that function as an effective solution to the inverse packing problem for given packing procedures and boundary conditions. Finally, we show that these results are verified by experiments on 3D-printed prototypes used to make packings in the real world.Keywords: Inverse Problems, Artificial Evolution, Packing Fraction, Anisotropic Particles * e-mail: mmiskin@uchicago.edu It is easy to appreciate the fact that granular aggregates can have different physical properties if the particle shapes are different. For example, it is known that the mechanical strength and stiffness of a granular packing are both influenced by particle shape 1-3 . This follows since particle geometry directly determines both how grains arrange themselves when packed and how stresses propagate throughout the aggregate [3][4][5] . Yet at present, there is no straightforward way to exploit this relationship and find shapes that produce aggregates with specific, desired stiffnessʼs and/or strengths.The same problem manifests itself when examining the transport properties of granular packings. Here, microscopic features like the structures of interstices and the number of contacts per particle exert a strong influence on macroscopic properties like fluid permeability 6, 7 and thermal/electrical conductivities 7,8 . Again, it is clear that these bulk properties are intimately connected with particle shape, while it remains unclear how to leverage this knowledge to select shapes that tailor aggregates to have preferred behaviors.The heart of this issue can be put into stark contrast with the two, deceptively similar, questions. First, "Are there particle shapes that pack randomly to different densities?" Clearly the answer is yes [9][10][11][12][13][14] . Yet change the question to "which particle shapes pack randomly to a density of X?" and a general answer is unknown.In short, there is an apparent disparity between the number of relationships linking particle shape to aggregate behaviors, and the capacity to transform these same relationships into design rules. In light of this, answering a question like the later one above is tantamount to inventing a method that generically solves the "inverse problem" of associating shape to response. For problems like this, an aggregateʼs behavior is pre-specified and the goal is to find a particle geometry that produces this behavior.For a given granular inverse problem, we believe a true so...

Rational design of nanomaterials from assembly and reconfigurability of polymer-tethered nanoparticles

“…Computation allows us to rapidly screen candidate blocks for targeted assemblies. New data science approaches, coupled with high performance computingenabled prediction of TNP self-assembly, promise to further expedite material design in this space, [95][96][97] in the spirit of the Materials Genome Initiative. [98] Tethered NPs and related structures hold a great deal of promise as candidate-building blocks for next generation materials.…”

Optimizing packing fraction in granular media composed of overlapping spheres

“…37 In prior work we found CMA-ES to deliver excellent performance in optimization problems ranging from the packing of granular materials 24,25 to directed self-assembly of copolymers. 38,39 The evolutionary algorithm worked in concert with molecular dynamics simulations of 'virtual experiments,' providing input parameters to these simulations and updating the parameters according to the simulated outcome in relation to the optimization target (for details see Ref.…”

“…[1][2][3] Going beyond spherical particles, there has been much recent progress for polyhedral or polygonal shapes, [4][5][6][7][8][9] ellipsoids, cuboids, or 'superballs,' [10][11][12][13][14][15] cylinders, cones, and frustums of different aspect ratios, [16][17][18] as well as various types of particles constructed by joining disks or spheres. 11,[19][20][21][22][23][24][25] Furthermore, in the last few years, increasing attention has been paid to particles that are highly non-convex or are sufficiently flexible to assume non-convex shapes during the packing process. 14,[26][27][28][29][30][31][32][33][34] In almost all cases, these studies proceeded from a given particle type to find the packing density.…”

“…We tackle the above obstacles by using an approach developed recently by our group, 24,25 which treats the inverse problem as an optimization task within the context of artificial evolution. With this method, we turn the complex relationship between particle shape and packing density into a high-dimensional search landscape, where a physically accurate simulation generates a random packing and measures φ for a trial particle shape to be tested, and an efficient evolution algorithm mutates and updates this shape to maximize φ .…”

“…In our previous work, 24,25 particles of arbitrary shape were represented by a series of bonded spheres of varying radii, constrained to be touching at their contacting surfaces. With this shape representation, the particle type found by the optimizer to produce the densest random packing was a 3-sphere 'granular molecule' giving φ = 0.67 ± 0.03.…”