In the general case, elastic energy is given by the free energy per unit of volume f as a function of the strain tensor components ε ij f ( ε ε i j ) = 1 2 λ λ ε ε i i 2 + μ μ ε ε i j 2 where λ and μ are the Lamé elastic coefficients and we use Einstein summation convention. Noting the thermodynamic connection between stress tensor components and strain tensor components, σ σ i j = ( ∂ ∂ f ∂ ∂ ε ε i j ) T , where the subscript T denotes that temperature is held constant, then we find that if Hooke's law is valid, we can write the elastic energy density as f = 1 2 ε ε i j σ σ i j .