A unified anisotropic VDM–PFM theory for failure in fiber-reinforced composite materials

The currently emerging variational damage model theories for fracture analysis are limited to isotropic materials. To investigate the complex failure mechanisms of fiber-reinforced composites, a unified anisotropic VDM-PFM framework is proposed in this work. The unified anisotropic variational damage model model and new anisotropic phase-field model that constitute this framework are also proposed. The fracture dissipation functionals of the three proposed theoretical models depend on the ratio of the fracture toughnesss between the fiber and the matrix, the ratio of the length scale parameters, and the angle between the fiber normal and the damage gradient. This dependence endows the three theoretical models with a more comprehensive unity. The analytical solutions for Mode I fracture of the unified anisotropic variational damage model theory and the unified anisotropic phase-field model model are derived in the one-dimensional setting. An equivalent cohesive zone model developed from the unified variational damage model model is presented, and the coefficients of its constitutive functions are solved. Finally, through a series of representative numerical examples, the computational results of the current theoretical framework are shown to agree well with theoretical analyses and experimental results, demonstrating the effectiveness and accuracy of the proposed theoretical framework.