  We develop a thermodynamic framework for modeling nonlinear ultrasonic damage
sensing and prognosis in materials undergoing progressive damage. The framework
is based on the internal variable approach and relies on the construction of a
pseudo-elastic strain energy function that captures the energetics associated
with the damage progression. The pseudo-elastic strain energy function is
composed of two energy functions - one that describes how a material stores
energy in an elastic fashion and the other describes how material dissipates
energy or stores it in an inelastic fashion. Experimental motivation for the
choice of the above two functionals is discussed and some specific choices
pertaining to damage progression during fatigue and creep are presented. The
thermodynamic framework is employed to model the nonlinear response of material
undergoing stress relaxation and creep-like degradation. For each of the above
cases, evolution of the nonlinearity parameter with damage as well as with
macroscopic measurables like accumulated plastic strain are obtained.
