An extended gradient damage model for anisotropic fracture

This paper combines energy decomposition and an extended gradient damage (EGD) model to develop an anisotropic fracture framework with decoupling of tensile and shear cohesive laws. By introducing the shear-normal decomposition in the energy form, the driving force of the damage variable is established within the framework of the EGD model, which is then capable of capturing the traction-separation of potential crack surfaces in both shear and normal directions. The intrinsic correspondence between the cohesive law and the damage evolution enables the accurate prediction of anisotropic fracture behavior in the mixed form of Mode I and Mode II. Furthermore, the proposed model also addresses the damage unloading issue, which still remains a challenge in classic phase field theory or non-local damage theory. A number of numerical examples are presented as validation. Some cutting-edge benchmarks, such as complex mixed-mode fracture and perfect shear fracture, are well reproduced.