Non-differentiable energy minimization for cohesive fracture

Abstract eng:
A potential-based formulation for an initially rigid cohesive fracture model is proposed. The key feature is a term for the energy stored in the cohesive interfaces that is nondifferentiable at the origin. A consequence of this formulation is that the activation computation necessary in previous initially rigid formulations is now replaced by the computation of a minimizer of a nondifferentiable objective function. This immediately makes the method more amenable to implicit time stepping, since the activation criterion no longer interacts with the nonlinear solver for the next time step. The algorithm also sidesteps the complexities of time-discontinuity and tractionlocking previously observed in relation to initially rigid models. The optimization problem is reformulated as a nonlinear second-order cone programming problem. This reformulation allows the nondifferentiability created by the square-root terms in the potential to be treated in a well-understood conic programming framework and addressed with an interior point method.

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