The theory of generalized thermoelasticity with fractional order strain for dipolar materials with double porosity

Abstract

This article continues the work on dipolar thermoelastic materials, which are a special case of multipolar continuum mechanics. This theory allows a double-porous structure: a macro-porosity related to pores in the material and a microporosity, which shows fissures in the porous skeleton. This paper constructs a mathematical model for dipolar materials, which have a double-porosity structure by considering a fractional order Duhamel–Neumann stress–strain relation. The heat conduction is described by Cattaneo’s equations. The results are the constitutive equations of the linear theory of thermoelasticity with fractional order strain. The equations are valid for anisotropic materials and are called the Duhamel–Neumann equations with fractional order. Finally, the isotropic case is considered under the conditions of plane strain in order to perform some numerical simulations for samples of porous copper.