NEAR INCOMPRESSIBILITY AT UNIFORM TEMPERATURE OR ENTROPY IN ISOTROPICTHERMOELASTICITY

This article is concerned with longitudinal wave propagation in an iso tropic thermoelastic material that is nearly incompressible at either uniform temperature or uniform entropy. A dimensionless effective bulk modulus <(chi)over tilde> is defined such that <(chi)over tilde> --> infinity corresponds to incompressibility at uniform temperature. For 0 less than or equal to <(chi)over tilde> < 1, both longitudinal waves are stable, but for <(chi)over tilde> > 1, one is stable and the othe r unstable. If <(chi)over tilde> = 1, there is only one propagating mo de, and this is stable. Another dimensionless effective bulk modulus < (chi)over cap> is defined such that <(chi)over cap> --> infinity corre sponds to incompressibility at uniform entropy. For 0 less than or equ al to <(chi)over cap> < infinity, both longitudinal waves are stable. Making the identification <(chi)over cap> = <(chi)over tilde>/(1 - <(c hi)over tilde>), among others, enables the equivalence of the two type s of near constraint to be demonstrated. In particular, <(chi)over cap > --> infinity corresponds to <(chi)over tilde> --> 1(-), so that inco mpressibility at uniform entropy corresponds to near incompressibility at constant temperature. Many graphical results are presented to illu strate various points of theory.