Highly deformable (soft) particles

Mixtures of particles with different bulk properties are the constitutive element of many materials playing a crucial role in many natural and industrialprocesses. Among these materials are biological tissues composed of soft cells, foams, suspensions, clayey materials, powders and any sintered material as ceramic, metal, or pharmaceutical pills to name a few. In an engineering context, recent emerging issues have led to the design of new materials in the form of a mixture of soil particles with rubber pieces (made from discarded tires). The mechanical behavior of a packing of deformable particles mainly depends on the ability of the particles to both rearrange (sliding or rolling) and change their shape (related to the Young’s modulus and the Poisson’s ratio of the particles). For example, at the outset of compression, the granular assembly tends to the jammed state mainly by inner particle rearrangements until a mechanical equilibrium is reached withstanding the imposed loading. Once jammed, if the compression continues, the particle deformation is the main mechanism that permits the system to find a new mechanical equilibrium. Hence the complexity of rigid-deformable mix- tures arises from geometrical and mechanical dissimilarities between particles, leading to possible rearrangements even after the jamming point.

The compaction of soft granular matter, especially beyond the jamming point, is a broad issue increasingly studied in the literature. A large number of equations trying to link the confining pressure to the packing fraction φ (i.e., the ratio between the volume of the particles Vp over the volume of the box ) have been proposed, but most of them are based on empirical strategies. A major result that we already obtained is the introduction of a compaction model, free of ad hoc parameters, and standing on well-defined quantities related to (1) particle connectivity and (2) the bulk behavior of a single representative particle. Our model, derived from the micromechanical expression of the granular stress tensor, results in outstanding predictions of the compaction evolution for all values of the mixture ratio parameter at any friction.

Compaction of assembly of deformable, neo-hookean particles in 2D

Main articles

1] D. Cantor, M. Cardenas-Barrantes, I. Preechawuttipong, M. Renouf and E. Azéma, Compaction model for highly deformable particle assemblies, Phys. Rev. Letters 124, 208003 (2020). – Editors’ Suggestion –
2] M. Cardenas-Barrantes, D. Cantor, J. Barés, M. Renouf and  E. Azéma, Compaction of mixtures of rigid and highly deformable particles: A micromechanical model , Phys. Rev. E102, 032904 (2020)
3] M. Cardenas-Barrantes, D. Cantor, J. Barés, M. Renouf and E. Azéma, Micromechanical description of the compaction of soft pentagon assemblies , Phys. Rev. E, 103, 062902 (2021)
4] M. Cardenas-Barrantes, D. Cantor, J. Barés, M. Renouf and  E. Azéma, Three-dimensional compaction of soft granular packings , Soft Matter, 2021, 10.1039/D1SM01241J
5] Softer than soft: Diving into squishy granular matter, Papers in Physics vol 14 p 140009 (2022)
6] Experimental validation of a micromechanically based compaction law for mixtures of soft and hard grains, Phys. RevE, 106, L022901 (2022)
7] Compacting an assembly of soft balls far beyond the jammed state: Insights from three-dimensional imaging, Phys. RevE, 108, 044901 (2023)