Roger Fosdick

Aerospace Engineering and Mechanics
University of Minnesota
Minneapolis, MN 55455

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 solids, the analysis of this behavior is complicated by the fact that the full notion of stress and deformation gradient (as tensors), including shearing, must be considered, rather than simply the classical effects associated with pressure, specific volume, and temperature. In this work, I consider sequences of equilibrium coexistent phases, induced by thermal and mechanical loading, and the asymptotic limits and relations between various thermodynamic fields for elastic solids in the neighborhood of critical points. A generalized form of the famous Rushbrooke inequality from physical chemistry is obtained.