Analytical and numerical relaxation results for models in soil mechanics

TL;DR

This paper introduces a variational model for pressure-dependent plasticity in soil mechanics, providing explicit relaxation results and demonstrating well-posed numerical simulations with mesh-independent outcomes.

Contribution

It presents a novel variational formulation with an explicit quasiconvex envelope for pressure-dependent plasticity models, extending to higher dimensions empirically.

Findings

Explicit quasiconvex envelope for 1D model

Mesh-independent numerical results

Extension to higher dimensions empirically

Abstract

A variational model of pressure-dependent plasticity employing a time-incremental setting is introduced. A novel formulation of the dissipation potential allows one to construct the condensed energy in a variationally consistent manner. For a one-dimensional model problem, an explicit expression for the quasiconvex envelope can be found which turns out to be essentially independent of the original pressure-dependent yield surface. The model problem can be extended to higher dimensions in an empirical manner. Numerical simulation exhibit well-posed behavior showing mesh-independent results.