Numerical evaluation of the representative volume element for random composites

• Published in: European journal of mechanics, A, Solids Vol. 86; p. 104181
• Main Authors: El Moumen, A., Kanit, T., Imad, A.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.03.2021; Elsevier BV; Elsevier
• Subjects: Composite materials; Effective properties; Engineering Sciences; Homogenization; Mathematical models; Microstructures; Numerical homogenization; Porous materials; Representative volume element; Statistical characterization; Thermal conductivity; Thermal simulation; Thermodynamic properties; Statistical characterization; Representative volume element; Composite materials; Numerical homogenization; Microstructures; Effective properties
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2020.104181

The Representative Volume Element (RVE) plays a central role in the homogenization of random heterogeneous microstructures, especially for composite and porous materials, with a view to predicting their effective properties. A quantitative evaluation of its size is proposed in this work in linear elasticity and linear thermal conductivity of random heterogeneous materials. A RVE can be associated with different physical and statistical properties of microstructures. The methodology is applied to specific two–phase microstructure–based random sets. Statistical parameters are introduced to study the variation in the RVE size versus volume fractions of components and the contrast in their properties. The key notion of the integral range is introduced to determine these variations. For a given desired precision, we can provide a minimal volume size for the computation of effective mechanical and thermal properties. Numerical simulations are performed to demonstrate that a volume exists which is statistically representative of random microstructures. This finding is an important component for homogenization–based multiscale modeling of materials. •A quantitative evaluation of RVE size is proposed in this work in linear elasticity and linear thermal conductivity of random heterogeneous materials.•The methodology is applied to specific two–phase microstructure–based random sets. Statistical parameters are introduced to study the variation in the RVE size versus volume fractions of components and the contrast in their properties.•Numerical simulations are performed to demonstrate that a volume exists which is statistically representative of random microstructures.•This finding is an important component for homogenization–based multiscale modeling of materials.