Phase field method of composite material incorporating anisotropic constitutive behavior and orientation of strain energy release rate

Abstract The paper presents a phase field model for fracture analysis of fiber‐reinforced composite materials, considering the anisotropic critical strain energy release rate and constitutive relationship. Experimental results are used to verify the accuracy and effectiveness of the proposed model, enabling a comprehensive analysis of the fracture behavior under various conditions. It is discovered that by incorporating anisotropic structure tensor into the evolution equation derived from isotropic crack density form, a phase field model with weakly anisotropic fracture strain energy can be obtained. Furthermore, an anisotropic constitutive relationship accounting for tension‐compression asymmetry after material fracture is derived based on spherical‐partial decomposition of strain energy. The fracture behavior of composites under various conditions is systematically investigated through a series of numerical examples, including the tensile test of the central opening plate, the single‐sided notched plate, and an analysis of the influence of fiber arrangement. Additionally, it is highlighted that this model accurately describes non‐orthogonal two‐dimensional crack propagation in composite materials. Therefore, this model holds great potential in areas including design optimization and performance evaluation of composite materials. Highlights Both the anisotropic fracture strain energy and constitutive relationship are consideration. The stress and strain spherical‐partial decomposition for anisotropic constitutive relations are used. The present model allows simulation of fracture for composites with multiple fiber directions.