A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow

A coupled plastic damage model with two damage scalars is proposed to describe the nonlinear features of concrete. The constitutive formulations are developed by assuming that damage can be represented effectively in the material compliance tensor. Damage evolution law and plastic damage coupling are described using the framework of irreversible thermodynamics. The plasticity part is developed without using the effective stress concept. A plastic yield function based on the true stress is adopted with two hardening functions, one for tensile loading history and the other for compressive loading history. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction of the plastic hardening rate. The specific reduction factor is then deduced from the compliance tensor of the damaged material. Finally, the proposed model is applied to plain concrete. Comparison between the experimental data and the numerical simulations shows that the proposed model is able to describe the main features of the mechanical performances observed in concrete material under uniaxial, biaxial, and cyclic loadings.