Elastic microcracked bodies with random properties

Multi-Value Microstructural Descriptors for Complex Materials: Analysis of Ground States

“…In addition, when we want to analyze events connected with optical biaxiality, the introduction of the degree of prolation and the one of triaxiality of the molecular second-moment distribution is necessary. Beyond liquid crystals, higher moments of the distribution of microstructures can be useful descriptors of the local state of the matter in the cases of microcracked materials [40] and for granular assemblies in agitation [7]. Extending such a view to the general setting of the mechanics of complex materials has been tentatively pursued along different paths also in [66] and [38], in the latter case taking into account the possibility of migration of elements of a local family of microstructures, the one pertaining to the material element that we imagine placed at x.…”

Non-linear homogenization of polymer composites with porous inclusions

“…Material heterogeneity complicates even enormously the analysis unless we recognize a spatial scale (which can be even not unique) at which we can consider the material to have a statistically periodical structure. The presence of at least one such a scale justifies the notion of SRVE (see also [24,13,28,41,40]). Roughly speaking, the characteristic size of the SRVE should be chosen in such a way that the distribution of the inclusions within the SRVE can be considered statistically self-similar (also referred to as "statistically periodic").…”

Cohesive crack propagation in a random elastic medium

“…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.…”