Eigenfracture approximation of quasi-static crack growth in brittle materials

TL;DR

This paper introduces an eigendeformation approximation scheme for modeling quasi-static crack growth in brittle materials, demonstrating convergence to classical Griffith fracture evolution as the approximation parameter tends to zero.

Contribution

It proposes a novel variational approximation method using eigendeformations and proves its convergence to the classical crack evolution model.

Findings

The approximation scheme converges to Griffith's crack evolution as epsilon approaches zero.

The model incorporates irreversibility and energy balance in the crack growth process.

The approach provides a new variational framework for brittle fracture analysis.

Abstract

We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the displacement field and an eigendeformation field that approximates the crack in the material. By imposing a suitable irreversibility condition and adopting an incremental minimization scheme, we define a notion of quasi-static evolution for this model. We then show that, as $\varepsilon \to 0$, these evolutions converge to a quasi-static crack evolution for the Griffith energy of brittle fracture, characterized by irreversibility, global stability, and an energy balance.