A Shape Optimization Approach to Compute Fracture Propagation Paths in Tensile and Shear Benchmark Tests
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The problem of simulating brittle, quasi-static fracture propagation is a common numerical challenge and can be addressed using energy minimization techniques. Commonly-used methods include cohesive zone modeling and phase field methods. Recently, shape optimization techniques have been used to perform this energy minimization. Further challenges are posed by only considering tensile stress directions as physically motivated fracture propagation paths, which requires an additional eigenvalue decomposition of the strain tensor. This talk first focuses on the description of the minimization problem for brittle, quasi-static fracture propagation in a general setting. We then provide the minimization problem in a shape optimization setting. Finally, numerical simulations using shape optimization for commonly-used tensile and shear benchmark problems are also shown.
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