Compaction of mixtures of rigid and highly deformable particles: A micromechanical model

Compacting an assembly of soft balls far beyond the jammed state: Insights from three-dimensional imaging

Very soft grain assemblies have unique shape-changing capabilities that allow them to be compressed far beyond the rigid jammed state by filling void spaces more effectively. However, accurately following the formation of these systems by monitoring the creation of new contacts, monitoring the changes in grain shape, and measuring grain-scale stresses is challenging. We developed an experimental method that overcomes these challenges and connects their microscale behavior to their macroscopic response. By tracking the local strain energy during compression, we reveal a transition from granular-like to continuous-like material. Mean contact geometry is shown to vary linearly with the packing fraction, which is supported by a mean field approximation. We also validate a theoretical framework which describes the compaction from a local view. Our experimental framework provides insights into the granular micromechanisms and opens perspectives for rheological analysis of highly deformable grain assemblies in various fields ranging from biology to engineering.

Experimental validation of a micromechanically based compaction law for mixtures of soft and hard grains

In this Letter, we report on an experimental study which analyzes the compressive behavior of two-dimensional bidisperse granular assemblies made of soft (hyperelastic) and hard grains in varying proportions (κ is the portion of soft grains). By means of a recently developed uniaxial compression setup [Vu and Barés, Phys. Rev. E 100, 042907 (2019)]2470-004510.1103/PhysRevE.100.042907 and using an advanced digital image correlation method, we follow, beyond the jamming point, the evolution of the main mechanical observables, from the global scale down to the strain field inside each deformable grain. First, we validate experimentally and extend to the uniaxial case a recently proposed micromechanical compaction model linking the evolution of the applied pressure P to the packing fraction ϕ [Cantor et al., Phys. Rev. Lett. 124, 208003 (2020)]0031-900710.1103/PhysRevLett.124.208003. Second, we reveal two different linear regimes depending on whether the system is above or below a crossover strain unraveling a transition from a discrete to a continuous-like system. Third, the evolution of these linear laws is found to vary linearly with κ. These results provide a comprehensive experimental and theoretical framework that can now be extended to a more general class of polydisperse soft granular systems.

Three-dimensional compaction of soft granular packings

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.

Micromechanical description of the compaction of soft pentagon assemblies

We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons with packings of soft circular particles. We characterize the evolution of the packing fraction, the elastic modulus, and the microstructure (particle rearrangement, connectivity, contact force, and particle stress distributions) as a function of the applied stresses. Both systems behave similarly: the packing fraction increases and tends asymptotically to a maximum value ϕ_{max}, where the bulk modulus diverges. At the microscopic scale we show that particle rearrangements occur even beyond the jammed state, the mean coordination increases as a square root of the packing fraction, and the force and stress distributions become more homogeneous as the packing fraction increases. Soft pentagons experience larger particle rearrangements than circular particles, and such behavior decreases proportionally to the friction. Interestingly, the friction between particles also contributes to a better homogenization of the contact force network in both systems. From the expression of the granular stress tensor we develop a model that describes the compaction behavior as a function of the applied pressure, the Young modulus, and the initial shape of the particles. This model, settled on the joint evolution of the particle connectivity and the contact stress, provides outstanding predictions from the jamming point up to very high densities.

Highly strained mixtures of bidimensional soft and rigid grains: an experimental approach from the local scale

Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D bidisperse systems made of both soft and rigid grains. By means of a recently developed experimental set-up, from the measurement of the displacementfield we can follow all the mechanical observables of this granular medium from the inside of each particle up-to the whole system scale. We are able to detect the jamming transition from these observables and study their evolution deep in the jammed state for packing fractions as high as 0.915. We show the uniqueness of the behavior of such a system, in which way it is similar to purely soft or rigid systems and how it is different from them. This study constitutes thefirst step toward a better understanding of mechanical behavior of granular materials that are polydisperse in terms of grain rheology.

Bulk modulus of soft particle assemblies under compression

Using a numerical approach based on the coupling of the discrete and finite element methods, we explore the variation of the bulk modulus K of soft particle assemblies undergoing isotropic compression. As the assemblies densify under pressure-controlled boundary conditions, we show that the non-linearities of K rapidly deviate from predictions standing on a small-strain framework or the, so-called, Equivalent Medium Theory (EMT). Using the granular stress tensor and extracting the bulk properties of single representative grains under compression, we propose a model to predict the evolution of K as a function of the sample’s solid fraction and a reference state as the applied pressure P→0. The model closely reproduces the trends observed in our numerical experiments confirming the behavior scalability of soft particle assemblies from the individual particle scale. Finally, we present the effect of the interparticle friction on K’s evolution and how our model easily adapts to such a mechanical constraint.