Achieving irreversibility in damage evolution: Extended gradient damage model with decoupled damage profile and cohesive law

The irreversibility of damage evolution is a cornerstone of classical damage mechanics. Unfortunately, the existing gradient damage models in the literature cannot always fulfill this critical condition. Therefore, the Extended Gradient Damage (EGD) model is proposed in the present work in response to this challenge. In the EGD model, the governing equation of damage evolution is developed in the form that the damage evolution and cohesive law are fully decoupled. Thus, the irreversible damage evolution could be easily established by defining a well-behaved damage profile function without any intervention from cohesive law. Other than that, complex cohesive laws for different materials could be well captured in the EGD model with the help of the integral transformation technique. Moreover, the variational form of the proposed EGD model is developed by taking advantage of the dissipative force term, and the principle of thermodynamics is proven to be fulfilled. In the end, the proposed EGD model is validated by four numerical examples.