A one-dimensional spot welding model.
Andrews, K.T., Guessous, L., Nassar, S., Putta, S.V., Shillor, M. (2006)
Journal of Applied Mathematics
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Andrews, K.T., Guessous, L., Nassar, S., Putta, S.V., Shillor, M. (2006)
Journal of Applied Mathematics
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Doležel, Ivo, Šolín, Pavel, Ulrych, Bohuš
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R. Král, Pavel Lukáč (1998)
Acta Universitatis Carolinae. Mathematica et Physica
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Takeshi Takaishi, Masato Kimura (2009)
Kybernetika
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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 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. ...