Verification of a Two-Way Coupled Multiscale Finite Element Code for Dynamic/Impact Problems

Abstract

Engineering applications are increasingly facing structural challenges. Restrictive economic constraints and more complex geometric design have led to the use of advanced materials, such as fiber-reinforced composites. The behavior of such materials is governed by their microstructure, thus demanding the use of multiscale approaches. The present article aims at the verification of a two-way coupled multiscale finite element code previously developed by the authors. A two-scale analytical solution for a functionally graded elastic material subject to dynamic loads is herein derived in order to verify the multiscale code. Comparisons to overkilled single scale finite element solutions are also presented.

Keywords:

• multiscale modeling
• homogenization
• heterogeneous media
• verification
• finite element code

Acknowledgments

The authors gratefully acknowledge the financial support received from the US Army Research Laboratory under contract No. W911NF-04-2-00-11. The first author also acknowledges the financial support received from Conselho Nacional de Desenvolvimento Cientifico e Tecnologico - CNPq/Brazil under contract No. 200372/2006-8.