“…As such, a probabilistic approach is needed in order to evaluate the probability density function of the response, in view, for example, of an estimate of the reliability of the structure [12]. Furthermore, when considering the microscopic origin of the crack formation, homogenization techniques are usually applied to model a standard continuum which behaves like the originally micro-cracked body [13,14]. It is, therefore, of interest to check the hypothesis of a homogenized random field by evaluating the influence of the spatial variability of the material properties on the response.…”