A Bayesian estimation method for variational phase-field fracture problems

TL;DR

This paper introduces a Bayesian parameter estimation framework for phase-field fracture problems, enabling uncertainty quantification and efficient fitting of material parameters on coarse meshes, validated through numerical examples.

Contribution

It presents a novel Bayesian approach for estimating fracture parameters in phase-field models, reducing computational costs and handling uncertainties effectively.

Findings

Bayesian inversion accurately estimates material parameters.

The method reduces computational costs by using coarse meshes.

Numerical examples validate the approach's effectiveness.

Abstract

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian framework. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently small mesh) as the replacement of measurement will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependency of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. The obtained load-displacement curve that is usually the target function is matched with the reference values. Finally, our algorithmic approach is substantiated with several numerical examples.