Numerical implementation of the variational formulation for quasi-static brittle fracture

Authors

Blaise Bourdin, Louisiana State University

Document Type

Article

Publication Date

1-1-2007

Abstract

This paper presents the analysis and implementation of the variational formulation of quasi-static brittle fracture mechanics proposed by G. A. Francfort and J.-J. Marigo in 1998. We briefly present the model itself, and its variational approximation in the sense of Γ-convergence. We propose a numerical algorithm based on Alternate Minimizations and prove its convergence under restrictive assumptions. We establish a new necessary condition for optimality for the entire time evolution from which we derive the Backtracking algorithm. We give some elements of analysis of the Backtracking algorithm on a simple problem. We present realistic numerical simulations of a traction experiment on a fiber-reinforced matrix, and of the propagation of cracks in a perforated sample under mode-I loading. © European Mathematical Society 2007.

Publication Source (Journal or Book title)

Interfaces and Free Boundaries

First Page

411

Last Page

430

Recommended Citation

Bourdin, B. (2007). Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces and Free Boundaries, 9 (3), 411-430. https://doi.org/10.4171/IFB/171