A cross-property relation between the tensile modulus and the thermal conductivity of porous materials

Abstract Elastic moduli and thermal conductivity are key properties determining a material's response to mechanical deformations and temperature gradients. Although in the case of heterogeneous materials the effective properties are uniquely determined by the material's microstructure, in the case of porous materials, due to the large difference in the phase properties, it is usually not possible to predict the porosity dependence of any of these properties based on volume fraction information alone. Thus, for real-world materials experimental measurement is often considered to be the only feasible way to obtain a reliable porosity dependence for the property in question. Here we show, however, that for isotropic materials either the relative tensile modulus E r or the relative thermal conductivity k r can be calculated from the other via the cross-property relation 3 ln E r = 4 ln k r , as soon as one of them has been measured.