Probabilistic-based analysis and model selection of the tangential stiffness reduction : displacement curves of nonconforming contacts

Granular materials are of interest in a broad range of applications and the use of discrete-based numerical tools has been proved very promising in obtaining insights into their complex behavior. In discrete-based numerical analysis, the interface constitutive behavior of grain-to-grain systems is a key input, however, the recent literature suggests that there are significant discrepancies of the contact parameters of granular systems as obtained from micromechanical-based experiments adding significant uncertainties in contact mechanics modeling and the selection of input parameters. Thus, a probabilistic-based approach in the analysis of grain-scale experimental data constitutes a promising direction to deal with these high discrepancies. In the present study, we propose a probabilistic-based approach in the analysis and identification of the best-suited models of the tangential force—displacement law of sand grain contacts, and we demonstrate that the new approach outperforms that of traditional methods used in contact mechanics modeling providing a robust basis in discrete-based numerical simulations of particulate matter and problems involving powders and grains. Three different hyperbolic models and the Mindlin and Deresiewicz model were accordingly modified from their original versions to suit the purpose of contact mechanics analysis and the use of secant stiffness, rather than tangent stiffness as commonly employed. Objective criteria were implemented in the optimization and selection of the most appropriate model for each individual experimental curve analyzed in the present study. One of the important findings was that the effectiveness of each model depends on whether the grains at their contacts display steady-state sliding or micro-slipping. This could be particularly important to be considered in medium and large deformation problems where the contact displacements in the tangential direction are expected to exceed the micro-slip threshold.