77 New Thermodynamic Identities among Crystalline Elastic Material Properties Leading to a Shear Modulus Constitutive Law in Isotropic Solids

TL;DR

This paper derives 77 new thermodynamic identities relating elastic properties of crystalline solids, leading to a novel shear modulus constitutive law for isotropic materials, enhancing understanding of their elastic behavior.

Contribution

It introduces a comprehensive set of thermodynamic identities and a new shear modulus law based on strain volumes for crystalline elastic materials.

Findings

77 new thermodynamic identities established.

A new shear modulus constitutive law derived.

Enhanced understanding of crystalline elastic properties.

Abstract

Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain.