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.
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The authors are very pleased to acknowledge support in part by Battelle/U.S. Army Research Office (ARO) Research Triangle Park, North Carolina, under grant number DAAH04-96-C-0086, and by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory Cooperative agreement number DAAH04-95-2-0003/contract number DAAH04-95-C-0008. The content does not necessarily reflect the position or the policy of the Government, and no official endoresement should be inferred. Support in part by Dr. Andrew Mark of the IMT Computational Technology Activity and the ARL/MSRC facilities is also gratefully acknowledged. Special thanks are also due to the CICC Directorate and the Materials Directorate at the US Army Research Laboratory, Aberdeen Proving Grounds, Maryland. Other related support in form of computer grants from the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota and the Doctoral Dissertation Fellowship from the University of Minnesota are also gratefully acknowledged.