Damage Effective Functions Described Based on Combination of Macro and Micro Damage Mechanics

Abstract

The model of Helmholtz free energy serves as the constitutive functional expression for a damaged material, and was expanded into Taylor's series with respect to some state variables εij and Ω, the generalized expressions of isotropic elastic damage constitutive equations and the damage strain energy release rate with a configuration of isotropic damage scale were derived directly from the second law of thermodynamics. From the aspect of relationship between the porosity and damage variable, the different influence to damage effective functions were discussed theoretically and some valuable conclusions were carried out from the variation of material properties. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome, and the method developed in this article can be applied to study different damage problems. It is shown that the applied method and obtained conclusions are useful to study the damage mechanics problems further.