Contact radius and curvature corrections to the nonlocal contact formulation accounting for multi-particle interactions in elastic confined granular systems

We present contact radius and curvature corrections to the nonlocal contact formulation that take into account multi-particle interactions in elastic confined granular systems. The nonlocal contact formulation removes the classical assumption of independent contacts by taking into account the interplay of deformations due to multiple contact forces acting on a single particle. The contact radius correction considers the components of these deformations that contribute to the inter-particle contact area. The curvature correction improves the description of the contacting surface profiles by including higher order terms in their Taylor series expansions. To validate the corrected formulation, we restrict attention to rubber spheres under different loading conditions, in the absence of gravitational forces, adhesion or friction. Specifically, we show that the predictions of contact force and radius are in remarkable agreement with finite-element simulations and experimental observations up to levels of deformation at which contact impingement occurs, which was not possible with the original elastic nonlocal contact formulation. Convergence of the curvature corrected formulation is observed at a four-term correction.