Parameter estimation of an anisotropic damage model for concrete using genetic algorithms

This article presents an anisotropic damage model for concrete that couples between elasticity and continuum damage mechanics. The formulation of constitutive model is based on the elastic strain energy in the framework of irreversible thermodynamics. The thermodynamic free energy is represented as a scalar function of elastic strain and damage tensors and used to derive the constitutive law and thermodynamic conjugate force of damage that is used to derive the dissipation potential. The damage evolution law is governed by the normality rule. The formulation of elastic strain energy of damaged material is capable of modeling the concrete anisotropic behavior under different loadings without decoupling the stress or damage release rate. A series of unknown parameters in the model formulation was used to control the constitutive behavior and damage surface. A Genetic algorithm FORTRAN subroutine is used to estimate these parameters based on the coupling between the constitutive and damage evolution equations. The performance of the damage model is verified with the experimental data from the literature. The model has shown a good agreement with the experimental results. It describes the anisotropy induced by the crack development within the concrete.