A GENERALIZED CROSS-PROPERTY RELATION BETWEEN THE ELASTIC MODULI AND CONDUCTIVITY OF ISOTROPIC POROUS MATERIALS WITH SPHEROIDAL PORES

Abstract

A new generalized cross-property relation is proposed for predicting the relative elastic moduli (Young's modulus, shear modulus, bulk modulus) from the relative conductivities (thermal or electrical) of isotropic porous materials with spheroidal pores. Using this cross-property-relation it is possible to estimate the elastic moduli when the conductivites are known (either from real-world measurements or from numerical calculations on digital microstructures) and vice versa. This generalized cross-property relation contains the case of spherical or isometric pores as a special case, but is sufficiently general to account for the properties of materials with strongly anisometric pores, i.e. randomly orientated prolate and oblate pores, including the extreme cases of pore channels or microcracks. The exponent of this cross-property relation is shown in graphical form and - for future reference with respect to practical applications - its numerical values are listed in tabular form as a function of the pore aspect ratio and the Poisson ratio of the solid

Keywords

• Elasticity
• Conductivity (thermal, electrical)
• Porosity
• Pore shape (prolate, oblate, isometric, anisometric, spherical, spheroidal)
• Pore channels
• Microcracks
• Aspect ratio
• Poisson ratio (Poisson number, non-auxetic)
• Elastic moduli (Young's modulus, tensile modulus, shear modulus, bulk modulus, compressive modulus)
• Cross-property relation
• Eshelby-Wu coefficient
• Maxwell coefficient