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We investigate the structural, vibrational, and mechanical properties ofjammed packings of deformable particles with shape degrees of freedom in threedimensions (3D). Each 3D deformable particle is modeled as asurface-triangulated polyhedron, with spherical vertices whose positions aredetermined by a shape-energy function with terms that constrain the particlesurface area, volume, and curvature, and prevent interparticle overlap. We showthat jammed packings of deformable particles without bending energy possesslow-frequency, quartic vibrational modes, whose number decreases withincreasing asphericity and matches the number of missing contacts relative tothe isostatic value. In contrast, jammed packings of deformable particles withnon-zero bending energy are isostatic in 3D, with no quartic modes. We findthat the contributions to the eigenmodes of the dynamical matrix from the shapedegrees of freedom are significant over the full range of frequency and shapeparameters for particles with zero bending energy. We further show that theensemble-averaged shear modulus $\langle G \rangle$ scales with pressure $P$ as$\langle G \rangle \sim P^{\beta}$, with $\beta \approx 0.75$ for jammedpackings of deformable particles with zero bending energy. In contrast, $\beta\approx 0.5$ for packings of deformable particles with non-zero bending energy,which matches the value for jammed packings of soft, spherical particles withfixed shape. These studies underscore the importance of incorporating particledeformability and shape change when modeling the properties of jammed softmaterials.

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