A rate-dependent stochastic damage–plasticity model for quasi-brittle materials

In this work, a rate-dependent model for the simulation of quasi-brittle materials experiencing damage and randomness is proposed. The bi-scalar plastic damage model is developed as the theoretical framework with the damage and the plasticity opening for further developments. The governing physical reason of the material rate-dependency under relatively low strain rates, which is defined as the Strain Delay Effect, is modeled by a differential system. Then the description of damage is established by further implementing the rate-dependent differential system into the random damage evolution. To reproduce the evolution of plasticity under a variety of stress conditions, a multi-variable phenomenological plastic model is proposed and the description of plasticity is then formulated. An explicit integration algorithm is developed to implement the proposed model in the structural simulation. The model results are validated by a series of numerical tests that cover a wide variety of stress conditions and loading rates. The proposed model and algorithm offer a package solution for the nonlinear dynamic structural simulations.