A rate-dependent phase-field framework for the dynamic failure of quasi-brittle materials

In recent years, phase-field theory has become an efficient approach for predicting damage and fracture of engineering materials. However, the rate-dependence of quasi-brittle materials is not considered in most exiting models. To address this issue, we develop a new phase-field damage model for the dynamic failure of quasi-brittle solids based on the microforce balance law, within which a linear viscoelastic constitutive relation in effective stress space and a hyperbolic phasefield evolution equation are incorporated. Then several representative numerical examples are presented to demonstrate the ability of the proposed model in characterizing the dynamic failure process of quasi-brittle solids. Good agreements are achieved between numerical predictions and theoretical and experimental results. In particular, the increase of tensile strength and the transition of failure modes of concrete-like materials with the increase of loading rates can be well reproduced.