On the convergence of 3D free discontinuity models in variational fracture
Free discontinuity problems arising in the variational theory for fracture mechanics are considered. A Γ -convergence proof for an r-adaptive 3D finite element discretization is given in the case of a brittle material. The optimal displacement field, crack pattern and mesh geometry are obtained through a variational procedure that encompasses both mechanical and configurational forces. Possible extensions to cohesive fracture and quasi-static evolutions are discussed.
KeywordsVariational fracture Free discontinuity models Γ -Convergence r-Adaption Configurational forces
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