A Universal Law for the Elastic Moduli of Solids and Structures

S. J. Burns, Department of Mechanical Engineering, University of Rochester

Hopeman 224

The elastic material properties of solids are generally thought to depend on stress, temperature and composition.  It is shown that zero-shear thermal expansion coefficients lead to either violations of the 2^nd law of thermodynamics or unstable material in shear.  Both of these options are unacceptable.  The point with zero-shear thermal expansion coefficients gives a second order differential equation for a universal, elastic, shear, compliance law.  Isothermal and adiabatic concepts are replaced with volume as the variable of choice for all elastic moduli in solids.  The shear and the bulk moduli of (all) solids are predicted with unerring accuracy by observing the elasticity as a specific volume power law.  The hypothesis is supported by experimental evidence from foams, Schneebeli 2-D graphene mats, metamaterials, fully dense metals, ceramics and minerals.  The proposed universal elastic moduli law is generalized but always describes materials that support shear stresses and elastic moduli that only depend on volume.  Finally, the role of energy per-unit-volume vs energy per-unit-mass is discussed for FEA or DFT systems.