Energy-based r-adaptivity: a solution strategy and applications to fracture mechanics |
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Authors: | Michael Scherer Ralf Denzer Paul Steinmann |
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Affiliation: | 1. Department of Mechanical Engineering, Applied Mechanics, University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany 2. Department of Mechanical Engineering, Applied Mechanics, University of Erlangen–Nürnberg, Egerlandstr. 5, 91058, Erlangen, Germany
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Abstract: | This paper deals with energy based r-adaptivity in finite hyperelastostatics. The focus lies on the development of a numerical solution strategy. Although the concept of improving the accuracy of a finite element solution by minimizing the discrete potential energy with respect to the material node point positions is well-known, the numerical implementation of the underlying minimization problem is difficult. In this paper, energy based r-adaptivity is defined as a minimization problem with inequality constraints. The constraints are introduced to restrict the maximum distortion of the finite element mesh. As a solution strategy for the constrained problem, we use a classical barrier method. Beside the theoretical aspects and the implementation, a numerical experiment is presented. We illustrate the performance of the proposed r-adaptivity in the case of a cracked specimen. |
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