A study on the thermoelasticity of three-phase-lag dipolar materials with voids

Abstract

With a wide applicability in solid state mechanics, the theory of continuous dipolar materials with voids is a distinctive part of microstructure theory, a theory that emerged with the necessity of eliminating the discrepancies between the classical theory and its experimental applications. These inconsistencies are caused by the influence of the microstructure of materials on the general deformations of the bodies, such as ceramics, graphite or polymers. In the present work, we study the mixed boundary value problem with initial data for the thermoelasticity of three-phase-lag dipolar materials with voids, in order to obtain the corresponding constitutive laws, using the same method as in the classical elasticity. By going deeper into the study of these materials, we achieve a uniqueness result and a reciprocal relation, using less common methods, like the dissipative inequality regarding the result of uniqueness. Along with these aspects, we demonstrate a variational principle for anisotropic and non-homogeneous materials, derived from a well-known variational principle, but studied in the context of thermoelasticity of three-phase-lag dipolar materials with voids.

Transversely isotropic visco‐thermo‐elastic nanobeam with time harmonic laser pulse and new modified three phase lag Green‐Nagdhi model

“…Kumar et al [7], Kumar & Kumar [8] examined the thermoelastic damping by using the TPL theory of thermoelasticity of a microbeam resonator. Codarcea-Munteanu & Marin [9] proposed a model for dipolar materials with TPL theory of thermoelasticity with voids. Abouelregal [10] proposed a novel model of TPL thermoelastic theory of higher-order using fractional calculus.…”

Influence of Geometric Equations in Mixed Problem of Porous Micromorphic Bodies with Microtemperature

“…The theory of porous materials, initially studied by Goodman and Cowin in [21], was subsequently deepened [22][23][24], being just a few examples of recent papers. First studies dedicated to the theory of bodies having microtemperatures were published by Grot, which created the foundation of this theory see, for instance [25], considering that the microelements of a continuous body are endowed with microtemperatures, along with microdeformations, thus extending existing theories of materials with inner structure.…”