On the existence of representative volumes for softening quasi-brittle materials – A failure zone averaging scheme

Abstract

a b s t r a c tThe concept of the representative volume element (RVE) for softening materials is revised in this contribution. It is demonstrated by means of numerical simulations that there exists a sample which is statistically representative for quasi-brittle materials with random microstructure like concrete. This finding is an important ingredient for homogenization-based multiscale modelling of softening materials.

Homogenization-based multiscale crack modelling: From micro-diffusive damage to macro-cracks

“…Note that the absence of a linear branch in the presented curves is due to the fact that the failure zone averaging should only be used after development of a failure band. Based on this observation plus a statistical analysis presented in [21], the authors have confirmed the existence of an RVE for quasi-brittle materials with random heterogeneous microstructure that exhibit localized failure with a continuum damage model. …”

“…In [21], the existence of an RVE for quasi-brittle materials (under tensile loading) with random complex heterogeneous microstructure exhibiting diffusive damage has been confirmed based upon a special averaging scheme, the failure zone averaging scheme, which filters out the linear contribution of the micro sample.…”

“…In [21], the authors have proposed a special averaging scheme which was named failure zone averaging scheme with which the existence of an RVE for random heterogeneous quasi-brittle materials in softening regime has been proved. For the sake of completeness, this averaging scheme is described shortly.…”

“…In this manuscript departing from the result reported in [21], we are going to derive cohesive laws, which are objective with respect to micro sample size, for softening materials with a random heterogeneous microstructure subjected to tensile, shear and mixed-mode loading. It is confirmed that an RVE does exist for softening materials with microstructures undergoing diffusive damage.…”

“…Details on the generation procedure of these samples can be found in [22]. Note that we have not considered bigger samples and different realizations since a statistical analysis of the existence of an RVE for this kind of material has already been given in [21].…”