The shear contribution to the equation of state: A universal law for the elastic moduli of solids

Cauchy's stress tensor, in the most generalized form, is known to be in two parts: a pressure plus octahedral shear stresses. Shear stress thermodynamics in pressurized and sheared systems are used to describe the physical shear properties of materials. Pressure alone does not fully describe solids although pressure is the basis for most equations of state. The thermal expansion coefficients are the major differences between normal and shear thermal strains. Shear-strain thermal expansion coefficients are central to predicting a material's shear prop-erties. Shear thermodynamics through the entropy-stress components predicts shear moduli proportional to a power-law in the specific volume. The concept is applied to all elastic moduli in solids and structures. Extensive empirical evidence supports elastic moduli that depend only on specific volume. The evidence is very extensive and leads to a new, generalized, universal, elastic moduli concept; it applies to materials that support shear stresses i.e., solids. A shear equation of state is explored in detail with use of empirical data. The elastic moduli are proportional to a specific volume power-law; the volume is both pressure and temperature dependent.