A direction-dependent smoothing gradient damage model for anisotropic brittle fracture

Abstract

We present a novel smeared gradient-enhanced damage model which takes into account direction-dependent damage evolution in two-dimensional brittle materials (e.g., uniaxial fiber-reinforced composites and polycrystalline materials). The recently developed smoothing gradient damage model for isotropic localized failure analysis is revisited by introducing a new damage evolution equation towards anisotropic fracture. To this end, the evolving anisotropic gradient interaction parameter existed in the damage evolution law is redefined by associating with a second-order structural tensor, aiming to possibly drive the directional fracture properties. This structural tensor restrains the crack growth in the direction of predefined fracture plane. In this circumstance, all cleavage or family of cleavage in a grain (for instance in polycrystalline materials) are assumed to be described by a single cleavage plane (or fiber plane) where the resistance of materials is considered to be weakest. Consequently, the directional dependency of cleavage fracture and transgranular fracture are captured precisely. This new definition utilized solely a scalar damage variable is in contrast to most other existing gradient damage models which usually employ multiple damage variables or higher-order gradient terms. Here, we also introduce an effective staggered algorithm aiming to reduce the computational cost, and its desirable features are demonstrated in the numerical experiments for transversely isotropic materials. The predicted crack paths in unidirectional fiber-reinforced composites and polycrystalline materials are in good agreement with reference results derived from other numerical methods.