A mean-strain estimate for plastic particles intended for distinct-particle simulations at high relative density

The kinematics of polydisperse granular materials comprised of overlapping spheres is carefully analysed. A single-particle strain estimate is developed that summaries the deformation experienced by each particle in terms of a mean deformation gradient. This strain estimate accounts for material displaced at interparticle contacts as well as a compensatory motion of the free particle surface. Forces that are work-conjugate to the mean deformation gradient are determined; they constitute the many-body forces required for a correct mechanical behaviour in the zero-porosity limit. Notwithstanding this, pairwise interparticle forces are needed for two main reasons; they dominate the particle interactions at small overlaps and stabilise the formulation in the continuum limit. Numerical simulations are performed to demonstrate the properties of the single-particle strain estimate and to test certain aspects of the formulation. In particular, it is demonstrated that the formulation can accommodate large rotations and provides a mechanical response consistent with that of a solid material in the zero-porosity limit. It is concluded that this work forms the basis for future developments aiming at formulation of realistic contact models for plastic particles and macroscopically consistent discrete methods for granular materials.