Energy-based r-adaptivity: A solution strategy and applications to fracture mechanics

Scherer, M., Denzer, R. and Steinmann, P. (2007) Energy-based r-adaptivity: A solution strategy and applications to fracture mechanics. International Journal of Fracture, 147(1-4), pp. 117-132. (doi: 10.1007/s10704-007-9143-9)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Scherer, M., Denzer, R., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal of Fracture
Publisher:Springer
ISSN:0376-9429
ISSN (Online):1573-2673
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