- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
9
2007
3
Numerical implementation of the variational formulation for quasi-static brittle fracture
Blaise
Bourdin
Louisiana State University, BATON ROUGE, UNITED STATES
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 $\Gamma$--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 simulation of a traction experiment on a fiber-reinforced matrix, and of the propagation of cracks in a perforated sample under mode-I loading.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
411
430
10.4171/IFB/171
http://www.ems-ph.org/doi/10.4171/IFB/171