Numerical simulation of a class of models that combine several mechanisms of dissipation: fracture, plasticity, viscous dissipation

TL;DR

This paper develops and analyzes numerical models that simulate the combined effects of fracture, plasticity, and viscous dissipation in geophysical materials, supported by theoretical proofs and 1D/2D numerical experiments.

Contribution

It introduces a formal framework for models with multiple dissipation mechanisms and demonstrates their validity through numerical simulations and a real-world analogue experiment.

Findings

Models satisfy a Clausius-Duhem inequality

Multiple dissipation regimes observed in simulations

Successful replication of geological indentation experiment

Abstract

We study a class of time evolution models that contain dissipation mech- anisms exhibited by geophysical materials during deformation: plasticity, viscous dissipation and fracture. We formally prove that they satisfy a Clausius-Duhem type inequality. We describe a semi-discrete time evolu- tion associated with these models, and report numerical 1D and 2D traction experiments, that illustrate that several dissipation regimes can indeed take place during the deformation. Finally, we report 2D numerical simulation of an experiment by Peltzer and Tapponnier, who studied the indentation of a layer of plasticine as an analogue model for geological materials.