Abstract
We use bi-dimensional non-smooth contact dynamics simulations to analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles. Deformable particles are modeled using the finite-element method and following a hyper-elastic neo-Hookean constitutive law. The evolution of the packing fraction, bulk modulus and particle connectivity, beyond the jamming point, are characterized as a function of the applied stresses for different proportion of rigid/soft particles and two values of friction coefficient. Based on the granular stress tensor, a micro-mechanical expression for the evolution of the packing fraction and the bulk modulus are proposed. This expression is based on the evolution of the particle connectivity together with the bulk behaviour of a single representative deformable particle. A constitutive compaction equation is then introduced, set by well-defined physical quantities, given a direct prediction of the maximum packing fractionφmaxas a function of the proportion of rigid/soft particles.
Highlights
The mixture of particles with different elastic properties is extensively observed in nature and in a great number of applications
For systems composed entirely of deformable particles there is a large number of equations that describe well their compaction behavior [9,10,11,12], but mostly reduced to different variations of the equation proposed by Heckel [13], which assumes a proportionality between the porosity and the packing fraction increment over the stress increment
We study the effect of the proportion of rigid-deformable particles in the mixture and the friction on the compaction evolution and the elastic properties beyond the jamming point
Summary
Where the sum runs over all the contacts enclosed by the volume V, with fic the ith component of the contact force at the contact c and c j the jth component of the vector joining the centers of particles interacting. Nc is the total number of contacts in the volume V, and the notation ... C stands for the average over the contacts. The mean stress is given by P = (σ1 + σ2)/2, with σ1 and σ2 the principal stress values. Assuming a small particle size dispersion around the diameter d and Z = 2Nc/Np, the coordination number, a microstructural equation for the compressive stress can be deduced [25]: P
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