Geodesic
Phase field model for mode III crack growth in two dimensional elasticity
Kybernetika, Tome 45 (2009) no. 4, pp. 605-614.

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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 $\epsilon >0$ 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.
Classification : 35K57, 35Q74, 74B20, 74R10, 81T80
Keywords: crack growth; phase field model; numerical simulation 
@article{KYB_2009__45_4_a4,
     author = {Takaishi, Takeshi and Kimura, Masato},
     title = {Phase field model for mode {III} crack growth in two dimensional elasticity},
     journal = {Kybernetika},
     pages = {605--614},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2009},
     mrnumber = {2588626},
     zbl = {1193.35007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a4/}
}
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Takaishi, Takeshi; Kimura, Masato. Phase field model for mode III crack growth in two dimensional elasticity. Kybernetika, Tome 45 (2009) no. 4, pp. 605-614. http://geodesic.mathdoc.fr/item/KYB_2009__45_4_a4/