Residual stress development in heterogeneous or composite materials is an important problem in manufacture process modeling. Composites possess an intricate microstructure in which the mismatch in thermal expansion coefficients between the fiber and matrix can lead to residual thermal stresses upon part cool-down. It is commonly assumed that prior to cool-down, the entire composite at both micro and macro length scales is at a zero stress temperature. As cool-down initiates, the mismatch in thermostress behavior and the mismatch in viscoelastic time-dependent behavior of the two phases lead to built-in residual stresses in the final product. A novel finite element approach is presented here for the coupled thermovisoelastic analysis of polymer-matrix composite structures containing microscopic heterogeneities. Due to its inherent advantages over other techniques, the asymptotic homogenization approach is employed to obtain the homogenized properties for use in the macroscale problem. For illustration, a simple Kelvin-Voight viscoelastic solid is studied to demonstrate the formulations involved in similar materials for which the time-dependent stress-strain relationship is subsequently homogenized. The formulation accounts for the dissipative corrector behavior for heterogeneous viscoelastic materials. An analytical solution for the degenerative homogeneous viscoelastic material subject to uniform thermal relaxation is employed to verify part of the formulations. Additional examples are shown to further illustrate the approach for more complex scenarios.
Bibliographical noteFunding Information:
Received 28 July 19,9ac9cepted 29 July 1999. The authors are very pleased to acknowledge support in part by Battelle/U.S. Army Reseach rOf¢ce (ARO) Reseach rTriangle Park, North Carolina, under gantrnumber 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 DAAH0-94-2-00035/contract number DAAH04-95-C-0008. The content does not necessarily re£ect the position or the policy of the Government, and no of¢cial endorsement 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 MerialsaDrtcteioe atrat the U.S. Army Research Laboratory, Aberdeen Proving Grounds, Maryland. Other related support in the form of coputmer grants frmotehMinnesota Supercomputer Institute (MSI), Minneapolis, Minnesota and the Doctoral Dissertation Fellowship from the University of Minnesota are also gratefully acknowledged. Address correspondence to Professor Kumar K. Tamma, Department of Mechanical Engineering, University of Minnesota, 111 Church Street SE, Minneapolis, MN 55455, USA
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