Development of a Nonperiodic Homogenization Method for One-Dimensional Continua

Report No. ARL-TR-3197
Authors: Michael J. Leamy, Peter W. Chung, and Raju Namburu
Date/Pages: May 2004; 20 pages
Abstract: This work describes a one-dimensional homogenization method that relaxes the usual assumption of periodicity of microscale displacements. As such, this method is appropriate for studying materials with periodic as well as nonperiodic microstructures. Expected applications for the new method include composite rods with manufacturing variability (where material periodicity is destroyed) and rods composed of functionally graded materials. The method is validated through direct comparison with a known exact solution, that being a rod with linearly varying axial rigidity. The method for this case is shown to be exact. Further application of the developed method to two different periodic materials is used to validate the usual periodic assumption employed in traditional homogenization methods.
Distribution: Approved for public release
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Last Update / Reviewed: May 1, 2004