Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industry

Abstract

Three-dimensional confocal images of two materials A and B from food industry made of two constituents with highly contrasted properties, having the same volume fraction but different morphologies, are used to estimate their effective elastic and thermal properties. For that purpose, finite element simulations based on explicit meshing of the microstructures are performed on six samples of the materials, with different boundary conditions: kinematic uniform (KUBC), stress uniform (SUBC) and periodic boundary conditions. Direct simulations on the entire samples show that KUBC and SUBC provide strongly different apparent properties, which rises the question of the representativity of the samples. A numerical and statistical computational homogenization methodology first proposed for random models of microstructures in [Kanit et al., Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids Struct. 40 (2003) 3647–3679] is extended here to the case of real microstructures in order to estimate the size of representative volume elements (RVE) for both materials. The samples of material A are found to be representative, whereas at least twice as large sample volumes would be necessary to predict the properties of material B with a precision of 5%. Numerical predictions of the effective properties using simulations on a large number of subdomains extracted from the samples with periodic boundary conditions are in satisfactory agreement with available experimental results. In particular, material A is twice as stiff as material B. This is due to a different percolation behaviour of the hard phase in the materials, which is investigated in the last section of the article. Indicators of geometrical and mechanical percolation, especially relevant for connected microstructures, are proposed and estimated using 3D image analysis.