Internal-interfacial cracking interaction: Combined phase-field and discontinuous Galerkin/cohesive zone modeling

Interaction simulations between internal and interfacial cracks arising in laminated composites have remained a challenging task in the computational mechanics community. Toward this end, this paper proposes a novel explicit approach that combines a length scale-insensitive phase-field model and a discontinuous Galerkin/cohesive zone model to respectively account for brittle or cohesive fracture of bulk materials and interfacial debonding. The presented approach advocates the incorporation of a discontinuous Galerkin term to overcome the artificial compliance problem inherent in existing phase-field methods that normally adopt intrinsic cohesive zone models for interfacial debonding. The capacity of our approach is further exploited by innovatively integrating the approach with an efficient six-node pentahedral solid-shell element, enabling a natural simulation of through-thickness cracks in thin shell structures with high-aspect-ratio elements. Implementation challenge, arising from the stress decomposition of the solid-shell element, of such integration is well addressed. In light of the considerable computational cost required for a phase-field-based method, the proposed approach is mapped to graphics processing units to improve the computational efficiency. Representative numerical examples have demonstrated the capability of the proposed approach in simulating mode-I and mixed-mode cohesive cracks, as well as brittle fractures in solids and shells. It is also shown that the presented approach is capable of effectively addressing the artificial compliance issue and capturing the competitive behavior between internal and interfacial cracks in a physically consistent manner.