Static and dynamic effective moduli of elastic-perfectly plastic granular aggregates under normal compression

Based on an existing simplified theoretical model for the normal contact interaction between two elastic-perfectly plastic spherical particles, we derived explicit expressions for the static and dynamic normal and dynamic tangential contact stiffnesses of elastic-perfectly plastic two-particle combination at pre-yield, yield, and post-yield conditions of normal loading. We used “static stiffness” or “loading stiffness” to refer to the slope of the force-displacement curve during monotonically increasing load. The “dynamic stiffness” or “unloading stiffness” refers to the stiffness that controls the speed of infinitesimal strain elastic waves propagating through the contacts. The static and dynamic contact stiffnesses are compared with numerical modeling of a two-sphere combination using the finite-element method. Furthermore, we used the explicit expressions for contact stiffnesses with the commonly used statistical averaging scheme to derive the static and dynamic effective bulk and shear moduli of a dry, random packing of identical elastic-perfectly plastic spherical particles. Elastic contact/mechanics-based effective medium models are unable to model the growth of contact area between inelastic (e.g., plastic) particles under normal force, which results in inaccurate predictions of contact stiffnesses and effective moduli. Once the particle reaches the limit of elasticity with onset of plastic deformation (yielding), further loading of two elastic-perfectly plastic spherical particles leads to a larger contact area than for two elastic particles under the same normal loading. As a result, after yielding, the dynamic effective moduli become stiffer than the corresponding moduli in the elastic case, whereas the static effective moduli remain constant, rather than increasing as in the elastic case.