Stress-based Effective Space Anisotropic Damage Model for Concrete

摘要

In this contribution a stress-based effective space anisotropic damage model is proposed and applied to concrete modeling. The general stress-based formulations of modeling anisotropic damage with a second-order tensorial damage variable are first discussed, and then the principle of damage dissipation equivalence is introduced to define the effective damage rate tensor by transforming the nominal damage rate tensor. Therefore obtained by the corresponding inverse transformation, the conjugated effective damage energy release rate is completely and simply expressed in the effective space and exhibits some convenient properties. The damage criteria can thus be thermodynamically consistently postulated in terms of the obtained effective damage energy release rates, after which the damage evolution law in the effective space is then established in accordance with the principal of maximum damage dissipation. By incorporating the positive and negative projection operators, the presented framework is generalized to take the unilateral effect into account. Finally the proposed model is applied to concrete modeling, leading to an anisotropic damage model which is capable of describing most of the nonlinear anisotropic behavior of concrete evident in the experiments while only requires six material properties with definitely physical meanings, I.e. the Young’s modulus, the Poisson’s ratio, the uniaxial tensile and compressive strength, and the Mode-I and Mode-II fracture energy.