Partial slip contact modeling of heterogeneous elasto-plastic materials

• Model for partial slip contact of heterogeneous elasto-plastic materials.
• Interactions among the contact bodies, the embedded inhomogeneity and plastic zone.
• Solutions of pressure distribution, tangential tractions, plastic zone and subsurface stress fields.
• Effects of a single inhomogeneity with various sizes, depths and yield strengths on the solutions.

In this study, a semi-analytic solution is developed for heterogeneous elasto-plastic materials under partial slip contact, and the effects of a single inhomogeneity embedded in the matrix material are investigated. The stick and slip areas are determined by an iterative conjugate gradient method with the assistance of the discrete convolution and fast Fourier transform algorithm. The inhomogeneities within a material are homogenized as homogeneous inclusions with properly determined eigenstrains based on the equivalent inclusion method, and the surface displacements induced by these eigenstrains along with those caused by the shear tractions are then introduced into the gap between the contact bodies to update surface geometry. The accumulative plastic deformation is iteratively obtained by a procedure involving a plasticity loop and an incremental loading process. The model takes into account the interactions among the contact bodies, the embedded inhomogeneities and the plastic zones, thus leading to an accurate solution of the surface pressure distributions, tangential tractions, plastic zones and subsurface stress fields. This solution is of great importance for the analysis of frictional heterogeneous contact coupling the normal and tangential behaviors in the elastic-plastic regime.