A new cell method, variational-asymptotic cell method (VACM), is developed to homogenize periodically heterogenous anisotropic materials based on the variational asymptotic method. The variational asymptotic method is a mathematical technique to synthesize both merits of variational methods and asymptotic methods by carrying out the asymptotic expansion of the functional governing the physical problem. Taking advantage of the small parameter (the periodicity in this case) inherent in the heterogenous solids, we can use the variational asymptotic method to systematically obtain the effective material properties. The main advantages of VACM are that: a) it does not rely on ad hoc assumptions; b) it has the same rigor as mathematical homogenization theories; c) its numerical implementation is straightforward because of its variational nature; d) it can calculate different material properties in different directions simultaneously without multiple analyses. To illustrate the application of VACM, a binary composite with two orthotropic layers are studied analytically, and a closed-form solution is given for effective stiffness matrix and the corresponding effective engineering constants. It is shown that VACM can reproduce the results of a mathematical homogenization theory.
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ASME 2005 International Mechanical Engineering Congress and Exposition
November 5–11, 2005
Orlando, Florida, USA
Conference Sponsors:
- Materials Division
ISBN:
0-7918-4234-7
PROCEEDINGS PAPER
A Variational-Asymptotic Cell Method for Periodically Heterogeneous Materials
Wenbin Yu
Wenbin Yu
Utah State University
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Wenbin Yu
Utah State University
Paper No:
IMECE2005-79611, pp. 15-24; 10 pages
Published Online:
February 5, 2008
Citation
Yu, W. "A Variational-Asymptotic Cell Method for Periodically Heterogeneous Materials." Proceedings of the ASME 2005 International Mechanical Engineering Congress and Exposition. Materials. Orlando, Florida, USA. November 5–11, 2005. pp. 15-24. ASME. https://doi.org/10.1115/IMECE2005-79611
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