Numerical Solution of Cohesive Crack Problems through Optimization Methods

1. Abstract We propose a novel approach for the analysis of cohesive crack propagation in elastic media. Unlike all existing methods that move from continuous displacement formulations that are properly enriched to handle the discontinuity, see e.g. the extended finite element method (XFEM) or the embedded discontinuity approaches, inherently discontinuous displacements and H(div,Ω) stresses in a truly mixed setting are herein proposed. The formulation, originally introduced to handle incompressible materials in plane elasticity, is herein extended to the analysis of propagating cohesive cracks in elastic media thanks to a novel variational formulation that is enriched with an interface energy term. Notably, no edge element is introduced but simply the inherent discontinuity of the displacement field is taken advantage of. Furthermore, stress flux continuity is imposed in an exact fashion within the formulation and not as an additional weak constraint as classically done. Extensive numerical simulations are presented to complete the theoretical framework. 2.