Thermodynamic Relations among Isotropic Material Properties in Conditions of Plane Shear Stress

Abstract

We present new general relationships among the material properties of an isotropic material kept in homogeneous stress conditions with hydrostatic pressure and plane shear. The derivation is not limited to the proximity of the zero shear-stress and -strain condition, which allows us to identify the relationship between adiabatic and isothermal shear compliances (inverse of the moduli of rigidity) along with new links, among others, between isobaric and isochoric shear thermal expansion coefficients, heat capacities at constant stress and constant shear strain. Such relationships are important for a variety of applications, including characterization of nanomaterials as well as identification of properties related to earthquakes precursors and complex media (e.g., soil) behaviors. The results may be useful to investigate the behavior of materials during phase transitions involving shear or in non-homogeneous conditions within a local thermodynamic equilibrium framework.