Prediction of the overall elastic behavior of composites by homogenization method

Abstract

The objective of this study was to determine the overall thermal elastic behavior of composites by homogenization method. The results obtained were compared with those by other well-known methods such as mean field method, self-consistent method and etc. A good agreement is achieved and thus a reliable method for predicting the effective behavior of composite is presented. It is very easy to extend this method to multi-phase composite. The material properties determined here include elastic modulus, Poisson ratio and thermal expansion coefficient (CTE).

Keywords

homogenization method / overall elastic behavior / composite

References

[1] Mori T, Tanaka K. Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions. Acta Metallurgica et Materialia, 1973, 21: 571-574.

[2] Hill R. A Self-Consistent Mechanics of Composite Materials. J. Mech. Phys. Solids, 1965, 13: 213-213.

[3] Mclaughlin R. A Study of the Differential Scheme for Composite Materials. Int. J. Engng. Sci., 1977, 15: 237-237.

[4] Mohammad Mohammadi-Aghdam.Micro-Mechanics of Unidirectional Metal Matrix Composites [Ph. D Dissertation]. University of Bristol, UK, 1999

[5] GUEDES Jose Miranda, KIKUCHI Noboru. Preprocessing and Postprocessing for Materials Based on the Homogenization Method With Adaptive Finite Element Methods. Computer Methods in Applied Mechanics and Engineering, 1990, 83: 143-198.

[6] C C Chamis. Simplified Composite Micromechanics Equations for Hygral, Thermal and Mechanical Properties.SAMPE Quarterly, April 1984:14–23

[7] Kikuchi N. An Optimal-Design Method of Microstructure Using the Homogenization Method. Transactions of the Materials Research Society of Japan, 1994, 16: 461-466.

[8] Hassani B, Hinton E. A Review of Homogenization and Topology Optimization I-Homogenization Theory for Media With Periodic Structure. Computers & Structures, 1998, 69(6): 707-717.

[9] Hassani B, Hinton E. A Review of Homogenization and Topology Optimization III-Topology Optimization Using Optimality Criteria. Computers & Structures, 1998, 69(6): 739-756.

[10] Zienkiewicz O C, Taylor R L. The Finite Element Method, 1989 Fourth Edition London: McGraw-Hill.

[11] Maocheng Wang, Min Shao. The Basic Principles and Numerical Methods of Finite Element Method, 1997 Beijing: Tsinghua University Press.

[12] Schapery R A. Thermal Expansion Coefficients of Composite Materials Based on Energy Principles. Journal of Composite Materials, 1968, 2: 380-384.

[13] Pirgon O, Wostenholm GH, Yates B. Thermal Expansion at Elevated Temperatures IV. Carbon-fiber Composites. J. Phys. D: Appl. Phys., 1973, 6(3): 309-321.