Acceleration Scheme for Nonlocal Gradient Damage Methods

There is a growing interest for using nonlocal damage mechanics type methods for modeling damage in solid mechanics, due to their practical implementation and ability to incorporate complex failure criteria. However, it is well known that the gradient damage methodology is computationally demanding, as it significantly increases the number of degrees of freedom in a system and requires the solution of a coupled system. In this study, we introduce a new acceleration method for localizing the gradient damage theory. Our approach adaptively modifies the number of degrees of freedom in the system, without altering the solution scheme, by introducing a criterion that adaptively switches between local and nonlocal formulations. The criteria is based on an integral approach and is applicable to both isotropic and anisotropic damage formulations, highlighting its versatility. The method is implemented in the finite element software ABAQUS by invoking several user modules. The performance of the acceleration scheme is validated through various numerical examples employing isotropic and anisotropic damage models. The results show that the scheme significantly reduces the computational cost of nonlocal gradient continuum damage analysis. Furthermore, it is shown that the acceleration does not affect the quality of the results.