An innovative truly-mixed method for cohesive-crack propagation problems

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) [Moës et al., 1999] or the

embedded discontinuity

[Jirásek, 2000] approaches, inherently discontinuous displacements and H(div) 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.