Variational Asymptotic Method for Unit Cell Homogenization
This article presents an overview of a recently developed micromechanics theory, namely, the variational asymptotic method for unit cell homogenization along with its companion code VAMUCH. It is emerging as a general-purpose micromechanics tool for predicting not only the effective properties of heterogeneous materials but also the local fields within the microstructure. The differences between VAMUCH and other micromechanics approaches are articulated. A simple realistic example is used to demonstrate it application in practical situations.
KeywordsRepresentative Volume Element Effective Property Effective Material Property Binary Composite Boron Fiber
The development of VAMUCH is supported, in part, by the National Science Foundation under Grant DMI-0522908 and the State of Utah Community/University Research Initiative Grant. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsement, either expressed or implied, of the funding agencies. The authors have also benefited much from the technical discussions with Drs. Victor Berdichevsky (Wayne State University, USA), Jacob Aboudi (Tel Aviv University, Israel), Brett A. Bednarcyk (NASA Glenn Research Center, USA), Todd O. Williams (Los Alamos National Laboratory, USA), and Herald Berger (University of Magdeburg, Germany), to whom we express our heartfelt appreciation. The authors also acknowledge the help of Mr. Zheng Ye in correcting Fig. 6.
- 6.Bensoussan A, Lions J, Papanicolaou G (1978) Asymptotic analysis for periodic structures, North-Holland, AmsterdamGoogle Scholar
- 7.Berdichevsky VL (1977) PMM 41:993–1006Google Scholar
- 8.Berdichevsky VL (1979) PMM 43:664–687Google Scholar
- 16.Kunin I (1982) Theory of elastic media with microstructure. Vols 1 and 2. Berlin, Springer-VerlagGoogle Scholar
- 18.Nemat-Nasser S, Hori M (1993) Micromechanics: Overall properties of heterogeneous materials, 2nd edn. North-Holland, AmsterdamGoogle Scholar
- 24.Tang T, Yu W (2008) Mech Adv Mater Struct (in press)Google Scholar
- 25.Tang T, Yu W (2009) Smart Mater Struct (submitted)Google Scholar
- 29.Yu W, Williams TO, Bednarcyk BA, Aboudi J, Tang T (2007) Proceedings of the 48th structures, structural dynamics and materials conference, April 23–26, Waikiki, HawaiiGoogle Scholar