On thermo-electro-viscoelastic relaxation functions in a Green–Naghdi type theory

Abstract

We find restrictions on the relaxation functions of thermo-electro-viscoelastic materials. This is achieved within an extension of the Green–Naghdi theory for thermoelasticity, which uses the energy equation to exploit constitutive equations. These restrictions extend the results previously found for thermo-viscoelastic materials and for the classical infinitesimal theory of viscoelasticity.

Keywords:

• Green–Naghdi continuum thermodynamics
• relaxation functions
• restrictions of relaxation functions
• thermodynamic restrictions
• thermo-electro-viscoelasticity
• viscoelasticity

Acknowledgment

The research leading to this work has been developed under the auspices of INDAM-GNFM, Italy.

Disclosure statement

The author declares that for the present article, there is no conflict of interest.

Notes

1 Remind that for a second- or fourth-order tensor A by $\mathit{A}\le 0$ ($\mathit{A}\ge \mathbf{0}$) we mean A is negative semi-definite (positive semi-definite). Accordingly, by $\mathit{A}\le \mathit{B}$ we mean $\mathit{A}-\mathit{B}$ is negative semi-definite.