Time-domain modeling of linear viscoelasticity using augmenting thermodynamic fields

A time-domain model of linear viscoelasticity is developed in terms of augmenting thermodynamic fields (ATF) that are coupled with the mechanical displacement field. Previous related efforts addressed time-domain finite element modeling of frequency-dependent material damping, but were effectively limited to one-dimensional stress states. The current work is based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. General coupled constitutive equations for the total and anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. The partial differential equations governing the temporal evolution of the total and anelastic displacement fields are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also discussed: the anelastic displacement field is effectively an internal field, as it cannot be directly affected by applied loads, but only through coupling to the total displacement. In order to illustrate the use of the method, ATF model parameters for a commonly-used high damping polymer are developed from available complex modulus data.