A mesoscale numerical approach to predict damage behavior in concrete basing on phase field method

In this paper, we develop a numerical approach to simulate the 2D complex damage and fracture process of quasi-brittle concrete materials. Based on the phase field theory for the case of elastic isotropic multicomponent materials and the generation process based upon Monte Carlo’s simulation method, we construct a numerical  procedure to solve complex damage thermodynamic problems. The diffusive phase field variable obtained from this calculation can be used to represent the crack nucleation and propagation within 2D complex mesostructure. Some factors that affect the numerical result (type of crack density function and type of split decomposition of strain energy) are accounted to make the predictions more accurate for the case of concrete material. Some new numerical examples are provided to show the usefulness of the approach.