A Discontinuous Finite Element Approximation of Quasi-static Growth of Brittle Fractures
نویسندگان
چکیده
منابع مشابه
A Discontinuous Finite Element Approximation of Quasi-static Growth of Brittle Fractures
We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffith’s criterion. We restrict our analysis to the case of anti-planar shear and we consider discontinuous displacements which are piecewise affine with respect to a regular triangulation.
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We define a notion of quasistatic evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi static growth of brittle fractures in linearly elastic bodies.
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We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith’s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although...
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We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo in [9]. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the prev...
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We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed in [13] by G. Dal Maso, G.A. Francfort, and R. Toader, which takes into account body forces and surface loads. We employ adaptive triangulations and prove convergence results for the total, elastic and surface energies. In the case in which the elastic energy is stric...
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ژورنال
عنوان ژورنال: Numerical Functional Analysis and Optimization
سال: 2003
ISSN: 0163-0563,1532-2467
DOI: 10.1081/nfa-120026378