Computing the effective crack energy of microstructures via quadratic cone solvers

Recently, mathematically well-defined homogenization results for the Francfort-Marigo fracture model were established. To solve the resulting cell formula, efficient computational methods were developed and improvements on solver and discretization techniques were investigated.

We discuss an approach for solving the governing cell formula based on a rewriting as a second order cone problem, a specific normal form for optimization problems. For such a formulation, potent high-accuracy optimization solvers are available. We demonstrate our approach on heterogeneous two-dimensional microstructures.