Representative Volume Element: Existence and Extent in Cracked Heterogeneous Medium

TL;DR

This paper develops modified periodic boundary conditions to improve the representativeness of RVE models in cracked heterogeneous composites, reducing size sensitivity and better capturing damage initiation at the microscale.

Contribution

It introduces a set of modified PBCs that mitigate size and mesh sensitivities in RVE modeling, enhancing the accuracy of microscale failure predictions in composites.

Findings

MPBCs reduce size dependency in RVE responses.

Analysis of 1200 RVEs shows improved damage prediction.

Damage initiation is influenced by fiber arrangement.

Abstract

Acknowledging the ever-increasing demand for composites in the engineering industry, this paper focuses on the failure of composites at the microscale and augmenting the use of multiscale modelling techniques to make them better for various applications. This work aims to increase the representativeness of the volume element by attenuating the mesh and size sensitivities in representative volume element (RVE) modelling. A technique to alleviate mesh sensitivity in RVE modelling is proposed, which equalises the fracture energy observed from computational analysis with the real phenomenon, thereby keeping the response independent of the bandwidth of strain localisation. Based on the hypothesis that ensuring periodicity of strain, in addition to displacement periodicity across the domain boundary and supplementing the capability of periodic boundary conditions (PBCs) to attenuate the size dependency in RVE modelling, a set of modified PBCs (MPBCs) are formulated. One thousand two hundred RVE samples falling into combinations of five fibre volume fractions and four RVE sizes are analysed under transverse loading, and the ability of MPBCs to attenuate the effect of RVE size on the precision of material response, particularly in the inelastic regime, is verified. This work also focuses on various factors affecting damage initiation in 2D composite RVEs. The arrangement of a pair of fibres with their members placed close to each other, such that the angle between the direction of loading and an imaginary line drawn between their centres is less, is observed to make the region between them more favourable to damage.