1. Solid Mechanics

Invited Lecture

COEXISTENT PHASES AND CRITICAL POINT BEHAVIOR IN THERMOELASTIC SOLIDS

ROGER FOSDICK
Aerospace Engineering and Mechanics
University of Minnesota
Minneapolis, MN 55455, USA

Abstract. Materials are known to behave in strange and novel ways in the neighborhood of criti cal points. The softening of various material moduli is commonly reported, and the smooth change of homogeneous states into complex multi phase 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 the thermodynamic fields of deformation gradient, temperature and the specific heat at constant deformation for elastic solids in the neighborhood of critical points. A generalized form of the famous Rushbrooke inequality from physical chemistry is obtained. Also, a generalized Clausius-Clapeyron equation is obtained.

Acknowledgement. This lecture was made possible through financial support from Pró-Reitoria de Pós-Graduação (PRPG/USP) and National Council for Scientific and Technological Development (CNPq).