Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics

An approach to modeling the mechanical behavior of fiber reinforced and unreinforced plastics with an evolving internal state is described. Intrinsic nonlinear viscoelastic and viscoplastic behavior of the resin matrix is taken into account along with growth of damage. The thermodynamic framework of the method is discussed first. The Gibbs free energy is expressed in terms of stresses, internal state variables (ISVs), temperature and moisture content. Simplifications are introduced based on physical models for evolution of the ISVs and on experimental observations of the dependence of strain state on stress state and its history. These simplifications include use of master creep functions that account for multiaxial stresses, environmental factors and aging in a reduced time and other scalars. An explicit representation of the strains follows, which is then specialized to provide three-dimensional homogenized constitutive equations for transversely isotropic, fiber composites. Experimental support for these equations is briefly reviewed. Finally, physical interpretation of some of the constitutive functions is discussed using results from a microcracking model as well as molecular rate process and free volume theories. It is shown that the present thermodynamic formulation leads to a generalized rate process theory that accounts for a broad distribution of thermally activated transformations in polymers.