On the Thermostatic Behavior of Coexistent Phases and Critical Point Analysis in Elastic Solids

Materials are known to behave in strange and novel ways in the neighborhood of critical points. The softening of various material moduli is commonly reported, and the smooth change of homogeneous states into complex multiphase microstructures is possible. For elastic solids, the analysis of this behavior is complicated because the full notion of the stress and deformation gradient tensor fields, including shearing, must be considered rather than simply the classical effects associated with pressure, specific volume, and temperature. Here, we are concerned with sequences of static (equilibrium) coexistent phases, induced by thermal and mechanical loading, and the asymptotic limits and relations between various thermodynamic fields for nonlinear elastic solids in the neighborhood of a critical point. (For fluids and gasses, see the works of Fisher (J. Math. Phys. 5:944–962, 1964), Fisher (Rep. Prog. Phys. 30:615–730, 1967), Griffiths (J. Chem. Phys. 43:1958–1968, 1965), and the monograph of Rowlinson and Swinton (Liquids and Liquid Mixtures. Butterworths Monographs in Chemistry. London, 1982).) A generalized form of the famous Rushbrooke inequality from physical chemistry is obtained.