MINIMUM SOLID AREA MODELS FOR THE EFFECTIVE PROPERTIES OF POROUS MATERIALS - A REFUTATION

Abstract

Minimum solid area (MSA) models are popular models for the calculation of the effective properties of porous materials and are frequently used to justify the use of a simple exponential relation for fitting purposes. In this contribution it is shown that MSA models, and the simple exponentials they support, are misleading and should be avoided. In particular, taking Young modulus and conductivity (thermal or electrical) as examples, it is shown that MSA models are based on the unjustified (and unjustifiable) hypothesis that the relative Young modulus and relative conductivity are identical, and moreover equal to the MSA fraction itself. This claim is generally false for isotropic materials, both random or periodic. Although indeed a very specific case exists in which this claim is true for the properties in one specific direction (viz., extremely anisotropic materials with translational invariance), in this specific case MSA models are redundant, because the relative properties are given exactly by the volume- or area-weighted arithmetic mean. It is shown that the mere existence of non-trivial cross-property relations is incompatible with the existence of MSA models. Finally, it is shown by numerical (finite-element) modeling that MSA models provide incorrect results even in the simplest of the cases for which they were originally designed, i.e. for simple cubic packings of partially sintered isometric (initially spherical) grains. Therefore, paraphrasing Box, MSA models are not only wrong, but also useless, and should be abandoned.

Keywords

• Minimum solid area / MSA model, Minimum contact area model, Cross-property relations, Thermal conductivity, Electrical conductivity, Porosity, Elastic moduli, Young modulus (tensile modulus)