Identifying Processes Governing Damage Evolution in Quasi-Static Elasticity. Part 2 -- Numerical Simulations

TL;DR

This paper develops and validates a numerical scheme combining Euler time discretization and finite element methods to simulate damage evolution in quasi-static elasticity, aligning well with theoretical predictions and physics.

Contribution

It introduces a new numerical framework using FEM and Euler schemes for damage modeling in Kachanov-type elasticity systems, validated through convergence and physical consistency.

Findings

Numerical scheme shows good agreement with physical behavior.

Convergence rate matches theoretical expectations.

Framework sets groundwork for damage process identification.

Abstract

We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type arguments to prove the consistency of the scheme as well as its convergence rate. We rely on the computational platform FEniCS to perform the FEM discretizations in space needed to compute the model output. The simulation results show a good agreement with both the physics of the problem and with our previous qualitative mathematical analysis results obtained for precisely the same problem setting. Furthermore, our implementation recovers nicely the theoretically expected convergence rate. This is a preliminary study preparing the framework for the rigorous numerical identification of the damage process in Kachanov-type models.