A finite element thermo-viscoelastic creep approach for heterogeneous structures with dissipative correctors

A finite element approach is presented for three-dimensional thermo-viscoelastic macro analysis of polymer-matrix composite structures containing micro-level heterogeneities, a two-scale approach. Due to its ability to account for microstructural details, the asymptotic expansion homogenization approach is employed to first, obtain the homogenized properties for use in the macroscale problem, and second, to study the local micro-level stress distributions influenced by macro effects. The theoretical formulations are described and developed for a thermoviscoelastic solid whose time-dependent stress–strain relationship can be homogenized. Arising from homogenization of the constitutive equation in the time domain is a hereditary dissipative corrector term. The dissipative corrector is time-dependent and accounts for heterogeneous behavior across the junction of dissimilar materials at the microstructural level. The additional term is necessary for the governing constitutive equations to satisfy equilibrium at both length scales. The objectives of this paper are three-fold: (1) develop the micro and macro constitutive equations for a thermoviscoelastic Kelvin–Voight material; (2) develop a computational approach for the constitutive equations; and (3) demonstrate and verify illustrative applications using results from the theoretical developments in the literature wherever available for a viscoelastic homogeneous/heterogeneous material.