Determination of the size of the representative volume element for random quasi-brittle composites

Abstract

a b s t r a c tA representative volume element (RVE) is related to the domain size of a microstructure providing a ''good" statistical representation of typical material properties. The size of an RVE for the class of quasi-brittle random heterogeneous materials under dynamic loading is one of the major questions to be answered in this paper. A new statistical strategy is thus proposed for the RVE size determination. The microstructure illustrating the methodology of the RVE size determination is a metal matrix composite with randomly distributed aligned brittle inclusions: the hydrided Zircaloy constituting nuclear claddings. For a given volume fraction of inclusions, the periodic RVE size is found in the case of overall elastic properties and of overall fracture energy. In the latter case, the term ''representative" is discussed since the fracture tends to localize. A correlation factor between the ''elastic" RVE and the ''fracture" RVE is discussed.

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

“…B€ ohm and Han [271] reported that when inelastic behavior of constituents is considered, larger sizes of the RVE are required compared to the estimates given in the literature for elastic composites. A similar conclusion was made by Pelissou et al [272] for quasi-brittle composites. The size of the RVE for nonlinear composites containing elastic rigid heterogeneities embedded in an elastoplastic or elastoviscoplastic matrix has been studied recently by Hoang et al [273].…”

Numerical homogenization of cracking processes in thin fibre-epoxy layers

“…In the longitudinal direction the length scale is varied by considering two different sample widths. Note that this approach is different from a convergence study on RVE's for bulk materials, where the length scales in all dimensional directions of the sample are varied, see for example, [9].…”

“…In the case of continuum models, numerical homogenization is based on computationally averaging the generated microstructural stress and deformation over a representative volume element (RVE), thereby implicitly (i.e., not in closed-form) establishing an effective, mesoscopic constitutive relation between the average stress and deformation. Over the past two decades, various approaches have been developed along this line, see for example [1,2,3,4,5,6,7,8,9]. These approaches rely on a local periodicity of the microstructure in the direct neighborhood of the RVE, but do not impose periodicity over the complete macroscopic structure under consideration (i.e., global periodicity is not required).…”

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

“…According to the former, a micro model with properly chosen dimension which is determined, for example, by the RVE's size quantification procedure given in [22,11,30], is numerically loaded at different loading conditions, the resulting cohesive laws are snapshot and later on used in a macroscopic FE computations as standard phenomenological constitutive laws 10 . In the spirit of the latter, there is a direct coupling between macro model and micro models.…”