A Thermodynamical Limitation on Compressibility

In their theory of thermostatics, Coleman and Noll have obtained a convexity inequality which places restrictions on admissible stress‐strain functions for elastic materials. Here we show that for an arbitrary elastic material in an arbitrary state of strain F, the general convexity inequality implies that the modulus of compression k obeys the inequality $\mathrm{k(F)\ge }\frac{2}{3}\mathrm{p̄(F)}$ where p̄ is the mean pressure, i.e. minus one‐third the sum of the principal stresses. Here k is defined to be the derivative of p̄ with respect to the mass density along a deformation process representing a uniform expansion from the state F.