Phase field modeling of crack propagation under combined shear and tensile loading with hybrid formulation

The crack phase field model has been well established and validated for a variety of complex crack propagation patterns within a homogeneous medium under either tensile or shear loading. However, relatively less attention has been paid to crack propagation under combined tensile and shear loading or crack propagation within composite materials made of two constituents with very different elastic moduli. In this work, we compare crack propagation under such circumstances modelled by two representative formulations, anisotropic and hybrid formulations, which have distinct stiffness degradation schemes upon crack propagation. We demonstrate that the hybrid formulation is more adequate for modeling crack propagation problems under combined loading because the residual stiffness of the damaged zone in the anisotropic formulation may lead to spurious crack growth and altered load-displacement response.