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

A finite element approach is presented for three-dimensional thermo-viscoel astic macro analysis of polymer-matrix composite structures containing micr o-level heterogeneities, a two-scale approach. Due to its ability to accoun t for microstructural details, the asymptotic expansion homogenization appr oach is employed to first, obtain the homogenized properties for use in the macroscale problem, and second, to study the local micro-level stress dist ributions influenced by macro effects. The theoretical formulations are des cribed and developed for a thermoviscoelastic solid whose time-dependent st ress-strain relationship can be homogenized. Arising from homogenization of the constitutive equation in the time domain is a hereditary dissipative c orrector 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 c onstitutive equations to satisfy equilibrium at both length scales. The obj ectives of this paper are three-fold: (1) develop the micro and macro const itutive equations for a thermoviscoelastic Kelvin-Voight material; (2) deve lop a computational approach for the constitutive equations; and (3) demons trate and verify illustrative applications using results from the theoretic al developments in the literature wherever available for a viscoelastic hom ogeneous/heterogeneous material. (C) 2000 Elsevier Science B.V. All rights reserved.