Decomposition of healing tensor: In continuum damage and healing mechanics

The decomposition of the healing variable (in the case of scalars) and the healing tensor (in the case of tensors) is carried out systematically and consistently. In this respect, the classical linear healing model is adopted in this work. The decomposition of healings includes the healing variable/tensor of cracks and the healing variable/tensor for voids. A third defect type is considered wherever mathematically possible. Thus a complete treatment of the decomposition of the healing tensor is presented covering both the one-dimensional and three-dimensional aspects. As an illustrative example, the case of plane stress, plane damage, and plane healing is solved. In this case, it is concluded that two distinct decomposition equations are obtained as well as one single coupling formula. The coupling equation is an expression that relates the various healing tensor components and damage tensor components for cracks and voids Furthermore; it is shown that there is no coupling in the one-dimensional case.

On damage tensor in linear anisotropic elasticity

In this paper, the anisotropic linear damage mechanics is presented starting from the principle of strain equivalence. The authors have previously derived damage tensor components in terms of elastic parameters of undamaged (virgin) material in closed form solution. Here, making use of this paper, we derived elasticity tensor as a function of damage tensor also in closed form. The procedure we present here was applied for several crystal classes which are subjected to hexagonal, orthotropic, tetragonal, cubic and isotropic damage. As an example isotropic system is considered in order to present some possibility to evaluate its damage parameters.

An Elastoplastic-anisotropic Damage Model for Concrete

An elastoplastic-anisotropic damage constitutive model for the description of nonlinear behavior of concrete is presented. The yield surface is developed in effective stress spaces, which takes into account the hardening effect and better match the experimental data. The stiffness degradation and softening effect are considered in the framework of continuum damage mechanics formulation. The second-order damage tensor is used to characterize the anisotropy induced by the orientation of microcracks. In order to simulate the unilateral effect, the elastic Helmholtz free energy is decomposed into a volumetric part and a deviatoric part. The different behavior under tensile and compressive loadings is modeled by using different variables in effective stress and damage tensor. Numerical results of the model accord well with experimental results at the material and structural levels.

On Determination of Geometric Damage Tensor

It is common to use the damage mechanics to study the deformation of fractured rock mass. The geometric damage tensor is always used to describe the effect of distributed joints on mechanical properties of rock mass. The disadvantages of the traditional determination method about geometric damage is that the natural section of rock mass, mining section and the measurement section are not perpendicular to each other. In this paper, a method combining with the probability theory and field scale line method is adopted to determine the geometric damage tensor. This method is convenient and fast. The solution of initial damage in damage evolution equation can be settled with this method. An effective proof is provided for the later analysis of damage stress of fractured rock mass.