A quasi-static model for craquelure patterns

TL;DR

This paper develops a phase-field model for the quasi-static evolution of crack patterns in brittle layers, providing theoretical insights and numerical validation that align with real craquelure patterns.

Contribution

It introduces a rigorous phase-field approach to model crack evolution and analyzes the transition layer influencing crack spacing, advancing understanding of pattern formation.

Findings

The model accurately predicts crack spacing in early stages.

Numerical results match observed craquelure patterns.

The transition layer controls initial crack development.

Abstract

We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the quasi-static evolution as the limit of time-discrete evolutions computed by an alternate minimization scheme. We study the limit evolution, providing a qualitative discussion of its behaviour and a rigorous characterization, in terms of parametrized balanced viscosity evolutions. Further, we study the transition layer of the phase-field, in a simplified setting, and show that it governs the spacing of cracks in the first stages of the evolution. Numerical results show a good consistency with the theoretical study and the local morphology of real life craquelure patterns.