Thermodynamic consistency of third grade finite strain elasticity

TL;DR

This paper develops a thermodynamically consistent framework for third grade finite strain elasticity, incorporating second gradient effects in stress and analyzing wave dispersion in isotropic materials.

Contribution

It introduces a thermodynamic approach to third grade elasticity with second gradient effects, deriving new constitutive relations and wave dispersion characteristics.

Findings

Third grade elastic materials with second gradient stress terms are formulated.

Dispersion relation for longitudinal plane waves in isotropic third grade materials is derived.

The framework ensures thermodynamic consistency of higher-order elastic models.

Abstract

Thermodynamic framework of finite strain viscoelasticity with second order weak nonlocality in the deformation gradient is investigated. The application of Liu procedure leads to a class of third grade elastic materials where the second gradient of the stress appears in the elastic constitutive relation. Finally the dispersion relation of longitudinal plane waves is calculated in isotropic materials.