THERMODYNAMIC CONSTITUTIVE-EQUATIONS FOR MATERIALS WITH MEMORY ON A MATERIAL TIME-SCALE

We present a complete, self-consistent set of thermodynamic constituti ve equations for viscoelastic solid and fluid materials which can be a pplied during arbitrary, three-dimensional deformations and thermal pr ocesses. Deformational and thermal histories are measured using a fadi ng memory norm in a material time which provides a quantitative indica tion of the constitutive models' ability to represent the dynamic resp onse. The free energy constitutive equation is a Frechet expansion abo ut the deformation and temperature histories of arbitrarily large but sufficiently slow departures from equilibrium in material time, The ki netic relationship between the laboratory and material time scales doe s not depend on equilibrium considerations. This approach greatly exte nds the applicability of low-order memory expansions to nonequilibrium polymer states. Constitutive equations for stress, internal energy, e ntropy, enthalpy, and heat capacity are derived. All the required mate rial properties can be evaluated unambiguously by independent experime nts via equilibrium and linear thermomechanical tests. Example predict ions illustrate (i) the isobaric volume relaxation as a rubber is cool ed into the glassy state, (ii) the yielding of a glassy solid polymer in uniaxial extension, (iii) non-Newtonian shear thinning during stead y shear of fluids, and (iv) stress overshoot of a polymer fluid in tra nsient shear. (C) 1996 Society of Rheology.