The Free Energy of Condensed Matter under Stress

Abstract

The currently accepted form of the free energy of condensed matter under stress, derived using the Helmholtz free energy, is disproved. Recognizing that the Gibbs free energy is the correct function of state, a new formula for the free energy density E which is linear–rather than quadratic–in the strain is derived. For isotropic and cubic media, the formula is E=-(c ₁₁+2c ₁₂)ε where the c _{i j} are elastic stiffness constants and ε is the strain. The formula is in accordance with published data.