Analytical and numerical relaxation results for models in soil mechanics

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 exhibits well-posed behavior showing mesh-independent results.

Automated summary

A variational model of pressure-dependent plasticity with a time-incremental setting is proposed. The dissipation potential is formulated in a novel manner to ensure variationally consistent condensed energy. For a one-dimensional model problem, an explicit expression for the quasiconvex envelope is derived, which is essentially independent of the original pressure-dependent yield surface. The model can be extended to higher dimensions empirically. Numerical simulation demonstrates well-posed behavior and mesh-independent results.