  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.
