Energetic solutions for the coupling of associative plasticity with damage in geomaterials

TL;DR

This paper establishes the existence of globally stable energetic solutions for a novel coupled model of associative plasticity and damage in geomaterials, offering a new approach to modeling such materials under compression.

Contribution

It introduces a new coupled model combining Drucker-Prager plasticity with damage, and proves the existence of energetic solutions for this model.

Findings

Existence of globally stable quasistatic evolutions proved.

The model couples plasticity with damage using advanced mathematical tools.

Provides a new framework for modeling geomaterials under compression.

Abstract

We prove existence of globally stable quasistatic evolutions, referred to as energetic solutions, for a model proposed by Marigo and Kazymyrenko in 2019. The behaviour of geomaterials under compression is studied through the coupling of Drucker-Prager plasticity model with a damage term tuning kinematical hardening. This provides a new approach to the modelling of geomaterials, for which non associative plasticity is usually employed. % The present coupling is such that The kinematical hardening is null where the damage is complete, so there the behaviour is perfectly plastic. We analyse the model combining tools from the theory of capacity and from the treatment of linearly elastic materials with cracks.