Mechanical response of packings of nonspherical particles: A case study of two-dimensional packings of circulo-lines

Zhang, Jerry; VanderWerf, Kyle; Li, Chengling; Zhang, Shiyun; Shattuck, Mark D.; O’Hern, Corey S.

doi:10.1103/physreve.104.014901

Cited by 4 publications

(5 citation statements)

References 41 publications

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“…Therefore, in anisotropic materials, it is important to track all Ĉ elements to fully characterize their mechanical properties. In this Appendix, we verify that the pressuredependence of the single-cell shear modulus is related to the variation of the packing fraction at jamming onset φ J with simple shear strain γ as shown in previous studies [37]. We illustrate this relationship using a single cell containing the N = 2 monodisperse disk packing with fixed-length walls in the inset to Fig.…”

Section: Discussionsupporting

confidence: 81%

“…As we showed previously for jammed packings of spherical particles with periodic boundary conditions, we find quite generally that G c (θ) varies linearly with p [15,37], G c (θ) = G c0 (θ)+λ c (θ)p, for disk-filled cells with periodic boundary conditions and physical walls in the absence of particle rearrangements (see the inset to Fig. 4 (a)).…”

Section: B Shear Modulus Versus Pressure For a Single Cellsupporting

confidence: 84%

“…In Appendix B, we derive the θ-dependence for all six stiffness matrix elements C ij , where C 33 gives the shear modulus for isotropic materials. In addition, our previous studies have shown that the sign of λ c (θ = 0) is determined by the second derivative of the packing fraction at jamming onset with respect to γ in jammed packings of spherical particles in periodic boundary conditions [15,37]. In Appendix C, we show that this relation is still true at any θ in disk-filled cells with fixed-length walls.…”

Section: B Shear Modulus Versus Pressure For a Single Cellsupporting

confidence: 52%

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Designing mechanical response using tessellated granular metamaterials

Jerry¹,

Wang²,

Jin³

et al. 2023

Preprint

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Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus G increases as a power-law in pressure p for static packings of spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase or decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct tessellated granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions, fixed-length walls, and flexible walls. Hypostatic jammed packings are found for disk-filled cells with flexible walls, but not in cells with periodic boundary conditions and fixed-length walls, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on p. We find that the slope of the shear modulus with pressure, λc < 0 for all packings in single cells with periodic boundary conditions where the number of particles per cell N ≥ 6. In contrast, single cells with fixed-length and flexible walls can possess λc > 0, as well as λc < 0, for N ≤ 16. We show that we can force the mechanical properties of multi-cell granular metamaterials to possess those of single cells by constraining the endpoints of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a novel platform for the design of soft materials with novel mechanical properties.

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Section: Discussionsupporting

confidence: 81%

Section: B Shear Modulus Versus Pressure For a Single Cellsupporting

confidence: 84%

Section: B Shear Modulus Versus Pressure For a Single Cellsupporting

confidence: 52%

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Designing mechanical response using tessellated granular metamaterials

Jerry¹,

Wang²,

Jin³

et al. 2023

Preprint

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“…Moreover, in all cases studied for which jammed particle packings (with repulsive linear spring interactions) possess quartic eigenmodes of the dynamical matrix, the power-law scaling exponent β > 0.5. For example, β ≈ 0.75 for 2D and 3D jammed packings of completely deformable particles [32], β ≈ 1.0 for 2D jammed packings of ellipse-shaped particles, and β ≈ 0.8-0.9 for 2D jammed packings of circulo-lines [55]. We encourage future studies to understand the link between quartic eigenmodes of the dynamical matrix and the non-trivial power-law scaling of G(P ) .…”

Section: Discussionmentioning

confidence: 91%

“…We find that G 0 decreases as A approaches unity (because of the decrease in z J as A → 1), but the power-law scaling exponents α ≈ 1 and β ≈ 0.75 (shown in the insets) are insensitive to A. Note that the power-law scaling exponent β is different for jammed packings of completely deformable particles compared to that for rigid spherical frictionless and frictional particles (β ≈ 0.5), as well as rigid, frictionless ellipse-(1.0) [23] and circulo-line-shaped particles (0.8-0.9) [55]. The larger values of β > 0.5 is correlated with the presence of quartic eigenmodes of the dynamical matrix.…”

Section: E Ensemble-averaged Shear Modulusmentioning

confidence: 97%

The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions

Wang¹,

Treado²,

Boromand³

et al. 2021

Preprint

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We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensembleaveraged shear modulus G scales with pressure P as G ∼ P β , with β ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, β ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.

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