An anisotropic gradient damage model with energy limiter for brittle crack propagation in composites

This work presents a novel anisotropic implicit gradient-enhanced damage model for directional fracture in composites with a single family of fibers. The improvement of anisotropy into the new smeared crack damage model is necessary and meaningful to adequately capture the typical orientation-dependent behavior of cracks in anisotropic media. Under the setting, the relationship between cracks and fiber direction is described through the introduction of a second-order structural tensor. This tensor depends on an anisotropic coefficient and the orientations of the fibers, which in turn control the direction of the simulated cracks. Consistently, the standard isotropic strain energy density function as the damage-driving term is replaced by the anisotropic SED function for the fiber-reinforced composites. With the use of the anisotropic SED function, a proper energy splitting technique is adopted for avoiding nonphysical damage under compression. The final governing equations of the equilibrium and anisotropic diffusive damage evolution equation are solved by means of the standard FEM with the aid of a staggered algorithm. The accuracy and modeling capacity of the developed direction-dependent fracture formulation are demonstrated through a set of representative numerical experiments. It shows that the anisotropic damage model can predict complex directional failure in transversely isotropic materials. •A novel anisotropic gradient damage model with energy limiter for brittle crack growth analysis.•The second-order structural tensor is adopted to describe the relationship between cracks and fiber direction.•An anisotropic strain energy density (SED) function is redefined for modeling the fiber- reinforced composites.•A series of representative numerical examples for anisotropic crack growth in composites are studied.•Accuracy and performance of the developed anisotropic damage theory are analyzed.