An energy release rate-based plastic-damage model for concrete

A new plastic-damage constitutive model for concrete is proposed in this paper. A tensile and a shear damage variable are adopted to describe the degradation of the macromechanical properties of concrete. Within the framework of continuum damage mechanics, the elastic Helmholtz free energy is defined to establish the plastic-damage constitutive relation with the internal variables. Regarding the specific format for the effective stress space plasticity, the evolution law for the plastic strains and the explicit expression for the elastoplastic Helmholtz free energy are determined and the damage energy release rates that are conjugated to the damage variables are derived. Thus, damage energy release ratebased damage criteria can be established in conformity to thermodynamical principles. In accordance with the normality rule, evolution laws for the damage variables are obtained to complete the proposed plastic-damage model. Some computational aspects concerning the numerical algorithm implementation are discussed as well. Several numerical simulations are presented at the end of the paper, whose results allow for validating the capability of the proposed model for reproducing the typical nonlinear performances of concrete structures under different monotonic and cyclic load conditions.