Stress-Based Effective Space Anisotropic Damage Model for Concrete

Abstract

Damage induced anisotropy is crucial for those initially isotropic materials, e.g., quasi-brittle materials such as concrete, geomaterials, ceramics, etc. Just as already pointed out by other researcher, at least second-order tensor should be adopted as damage variable to describe the damage induced anisotropy. Despite the substantial research efforts and the noteworthy recent contributions, the modeling of anisotropic damage is not a straight-forward task as that of isotropic one and still remains a challenging issue, among which the key point is the establishment of thermodynamically consistent damage evolution law. In this paper 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. The proposed model is applied to concrete modeling, leading to an anisotropic damage model which is capable of describingmost of the nonlinear anisotropic behavior of concrete evident in the experiments. It has been demonstrated that, only six material properties are required in the presented orthotropic damage model, i.e. the Young’s modulus E 0, the Poisson’s ratio v0, the uniaxial tensile and compressive strength f t and f c, and the Mode-I and Mode-II fracture energy G f I and G f II , to describe most of the nonlinear behavior evident in the experiments, such as the stiffness degradation, the strength softening, the enhancement of strength and ductility under compressive confinement, the strength decay induced by orthogonal tensile cracking, the unilateral effect under cyclic loading and the damage induced anisotropy, etc. Most importantly, all the parameters are physically meaningful and can be easily identified by conventional experiment procedures, which constitutes the main merit of the presented model over others existing in the literature.