International Journal of Fracture

, Volume 147, Issue 1–4, pp 117–132

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

• Michael Scherer
• Ralf Denzer
• Paul Steinmann
Original Paper

## 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.

## Keywords

Mesh optimization Hyperelasticity Constrained energyminimization Material forces Barrier method

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## Authors and Affiliations

1. 1.Department of Mechanical Engineering, Applied MechanicsUniversity of KaiserslauternKaiserslauternGermany
2. 2.Department of Mechanical Engineering, Applied MechanicsUniversity of Erlangen–NürnbergErlangenGermany