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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Scherer, M., Denzer, R., Steinmann, P. (2007). Energy-based r-adaptivity: a solution strategy and applications to fracture mechanics. In: Dascalu, C., Maugin, G.A., Stolz, C. (eds) Defect and Material Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6929-1_12
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DOI: https://doi.org/10.1007/978-1-4020-6929-1_12
Publisher Name: Springer, Dordrecht
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