Random anisotropic initial damage tensor

Abstract

Random initial damage can be described as isotropic, meaning that a random scalar value is employed to represent the uncertain initial state of damage. The prior pattern of micro-cracking at a point of an existing building or infrastructure, i.e., the initial damage, is oriented by an uncertain, mostly repeated, preload. Damage in such engineering structures shall therefore be considered as anisotropic and represented by a tensorial variable, in the form of a symmetric second-order tensor for the sake of practicality. In case of anisotropic damage, we formulate the uncertain initial damage in a probabilistic framework, in two steps: $\left(i\right)$ a probabilistic description of the tensor in its principal basis and $\left(ii\right)$ a probabilistic orientation of its principal basis. The effect of random initial damage on the tensile response of a quasi-brittle material, such as concrete, is quantified on the peak stress and various post-peak quantities of interest, using Random Continuum Damage Mechanics. The probabilistic response of the anisotropic damage model is computed, and the cumulative distribution functions of the quantities of interest are computed and analyzed. The way the anisotropy and misorientation of the principal basis of the initial damage tensor affect the uncertain mechanical response is quantified. Misorientation is particularly influential for uniaxial initial damage.