Particle Shape Effects

We present measurements of the stress response of packings formed from a wide range of particle shapes. Besides spheres these include convex shapes such as the Platonic solids, truncated tetrahedra, and triangular bipyramids, as well as more complex, non-convex geometries such as hexapods with various arm lengths, dolos, and tetrahedral frames. All particles were 3D-printed in hard resin. Well-defined initial packing states were established through preconditioning by cyclic loading under given confinement pressure. Starting from such initial states, stress–strain relationships for axial compression were obtained at four different confining pressures for each particle type. While confining pressure has the largest overall effect on the mechanical response, we find that particle shape controls the details of the stress–strain curves and can be used to tune packing stiffness and yielding. By correlating the experimentally measured values for the effective Young's modulus under compression, yield stress and energy loss during cyclic loading, we identify trends among the various shapes that allow for designing a packing's aggregate behavior.

Fig 1: Particle geometries. (a) Computer renderings (not to scale) and (b) photo of 3D-printed particles, after some use in the experiments. Top row (left to right): sphere, tetrahedron, cube, octahedron, dodecahedron, icosahedron. Middle row (left to right): truncated tetrahedron, triangular bipyramid, tetrahedral frame, dolo. Bottom row: jacks with arm length increasing to the right.

Fig 2: Ensemble-averaged stress–strain curves at σcon = 0.080 MPa. Solid lines represent averages of 3–5 independent tests for each shape. The half width of the shaded bands represents one standard deviation. The vertical order of the shapes drawn along the side, as well as the color of their outlines, corresponds to the large strain ordering of the curves (and their color.)