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Partial Regularity for Certain classes for Polyconvex functionals Related to Nonlinear Elasticity.

Martin Fuchs, Jürgen Reuling (1995)

Manuscripta mathematica

Phase field model for mode III crack growth in two dimensional elasticity

Takeshi Takaishi, Masato Kimura (2009)

Kybernetika

A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter $ϵ > 0$ and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.

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