Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T20:28:46.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Micromechanical Analysis of Heterogeneous Composites using Hybrid Trefftz FEM and Hybrid Fundamental Solution Based FEM

Published online by Cambridge University Press:  08 August 2013

C. Y. Cao ,
Q.-H. Qin  and
A. B. Yu
C. Y. Cao
Affiliation:
Research School of Engineering, Australian National University, Canberra, ACT 0200, Australia
Q.-H. Qin*
Affiliation:
Research School of Engineering, Australian National University, Canberra, ACT 0200, Australia
A. B. Yu
Affiliation:
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
*
*qinghua.qin@anu.edu.au
Get access

Abstract

In this paper, a new algorithm is developed based on the homogenization method integrating with the newly developed Hybrid Treffe FEM (HT-FEM) and Hybrid Fundamental Solution based FEM (HFS-FEM). The algorithm can be used to evaluate effective elastic properties of heterogeneous composites. The representative volume element (RVE) of fiber reinforced composites with periodic boundary conditions is introduced and used in our numerical analysis. The proposed algorithm is assessed through two numerical examples with different mesh density and element geometry and used to investigate the effect of fiber volume fraction, fiber shape and configuration on the effective properties of composites. It is found that the proposed algorithm is insensitive to element geometry and mesh density compared with the traditional FEM (e.g. ABAQUS). The numerical results indicate that the HT-FEM and HFS-FEM are promising in micromechanical modeling of heterogeneous materials containing inclusions of various shapes and distributions. They are potential to be used for future application in multiscale simulation.

Keywords

MicromechanicsRepresentative volume element (RVE)HT-FEMHFS-FEMFinite element method (FEM)Heterogeneous composite materialsEffective property
Type
Research Article
Information
Journal of Mechanics , Volume 29 , Issue 4 , December 2013 , pp. 661 - 674
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Mura, T., Micromechanics of Defects in Solids, 2nd Edition, Martinus Nijhoff, The Netherlands (1987).Google Scholar
2.S. Nemat-Nasser, M. H., Micromechanics: Overall Properties of Heterogeneous Materials, 2nd Edition, Elsevier Science, Amsterdam (1999).Google Scholar
3.Feng, X. Q., Mai, Y. W. and Qin, Q. H., “A Micro-mechanical Model for Interpenetrating Multiphase Composites,” Computational Materials Science, 28, pp. 486–493 (2003).Google Scholar
4.Qin, Q. H. and Yu, S. W., “Effective Moduli of Piezoelectric Material with Microcavities,” International Journal of Solids and Structures, 35, pp. 5085–5095 (1998).Google Scholar
5.Eshelby, J. D., “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 241, pp. 376–396 (1957).Google Scholar
6.Qu, J. and Cherkaoui, M., Fundamentals of Micromechanics of Solids, Wiley, Hoboken (2006).Google Scholar
7.Aboudi, J., Mechanics of Composite Materials: A Unified Micromechanical Approach, Elsevier, Amsterdam (1991).Google Scholar
8.Mori, T. and Tanaka, K., “Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions,” Acta Metallurgica, 21, pp. 571–574 (1973).CrossRefGoogle Scholar
9.Benveniste, Y., “A New Approach to the Application of Mori-Tanaka's Theory in Composite Materials,” Mechanics of Materials, 6, pp. 147–157 (1987).Google Scholar
10.Qin, Q. H., Mai, Y. W. and Yu, S. W., “Effective Moduli for Thermopiezoelectric Materials with Microcracks,” International Journal of Fracture, 91, pp. 359–371 (1998).Google Scholar
11.Ghosh, S., Bai, J. and Paquet, D., “Homogeniza-tion-Based Continuum Plasticity-Damage Model for Ductile Failure of Materials Containing Heterogeneities,” Journal of the Mechanics and Physics of Solids, 57, pp. 1017–1044 (2009).Google Scholar
12.Yang, Q. S. and Qin, Q. H., “Micro-Mechanical Analysis of Composite Materials By BEM,” Engineering Analysis with Boundary Elements, 28, pp. 919–926 (2004).Google Scholar
13.Yang, Q. S. and Qin, Q. H., “Modelling the Effective Elasto-Plastic Properties of Unidirectional Composites Reinforced by Fibre Bundles Under Transverse Tension and Shear Loading,” Materials Science and Engineering A, 344, pp. 140–145 (2003).Google Scholar
14.Seidel, G. D. and Lagoudas, D. C., “Micromechan-ical Analysis of the Effective Elastic Properties of Carbon Nanotube Reinforced Composites,” Mechanics of Materials, 38, pp. 884–907 (2006).CrossRefGoogle Scholar
15.Huang, Y., Hu, K. X. and Chandra, A., “Several Variations of the Generalized Self-Consistent Method for Hybrid Composites,” Composites Science and Technology, 52, pp. 19–27 (1994).Google Scholar
16.Qin, Q. H., “Micromechanics-BE Solution for Properties of Piezoelectric Materials with Defects,” Engineering Analysis with Boundary Elements, 28, pp. 809–814 (2004).Google Scholar
17.Chen, J. T., Lee, Y. T., Yu, S. R. and Shieh, S. C., “Equivalence Between Trefftz Method and Method of Fundamental Solution for the Annular Green's Function Using the Addition Theorem and Image Concept,” Engineering Analysis with Boundary Elements, 33, pp. 678–688 (2009).Google Scholar
18.Chen, J. T., Wu, C. S., Lee, Y. T. and Chen, K. H., “On The Equivalence of the Trefftz Method and Method of Fundamental Solutions for Laplace and Biharmonic Equations,” Computers and Mathematics with Applications, 53, pp. 851–879 (2007).Google Scholar
19.Qin, Q. H., “Trefftz Finite Element Method and its Applications,” Applied Mechanics Reviews, 58, pp. 316–337 (2005).CrossRefGoogle Scholar
20.Jirousek, J., Wroblewski, A., Qin, Q. H. and He, X. Q., “A Family of Quadrilateral Hybrid-Trefftz P-Elements for Thick Plate Analysis,” Computer Methods in Applied Mechanics and Engineering, 127, pp. 315–344 (1995).Google Scholar
21.Qin, Q. H., The Trefftz Finite and Boundary Element Method, WIT Press, Southampton (2000).Google Scholar
22.Qin, Q. H., “Solving Anti-Plane Problems of Piezoelectric Materials by the Trefftz Finite Element Approach,” Computational Mechanics, 31, pp. 461–468 (2003).Google Scholar
23.Dhanasekar, M., Han, J. J. and Qin, Q. H., “A Hybrid-Trefftz Element Containing an Elliptic Hole,” Finite Elements in Analysis and Design, 42, pp. 1314–1323 (2006).Google Scholar
24.Wang, H. and Qin, Q. H., “Fundamental-Solution-Based Finite Element Model for Plane Orthotropic Elastic Bodies,” European Journal of Mechanics, A/Solids, 29, pp. 801–809 (2010).Google Scholar
25.Wang, H. and Qin, Q. H., “Special Fiber Elements for Analyzing Thermal Behavior and Effective Properties of Fiber-Reinforced Composites,” Engineering Computations, 28, pp. 1079–1097 (2011).CrossRefGoogle Scholar
26.Zohdi, T. I. And Wriggers, P., An Introduction to Computational Micromechanics, Springer Verlag, Berlin (2004).Google Scholar
27.Miehe, C., “Computational Micro-To-Macro Transitions for Discretized Micro-Structures of Heterogeneous Materials at Finite Strains Based on the Minimization of Averaged Incremental Energy,” Computer Methods in Applied Mechanics and Engineering, 192, pp. 559–591 (2003).Google Scholar
28.Qin, Q. H. and Swain, M. V., “A Micro-Mechanics Model of Dentin Mechanical Properties,” Biomaterials, 25, pp. 5081–5090 (2004).Google Scholar
29.Huet, C., “Application of Variational Concepts to Size Effects in Elastic Heterogeneous Bodies,” Journal of the Mechanics and Physics of Solids, 38, pp. 813–841 (1990).CrossRefGoogle Scholar
30.Hazanov, S. and Huet, C., “Order Relationships for Boundary Conditions Effect in Heterogeneous Bodies Smaller Than the Representative Volume,” Journal of the Mechanics and Physics of Solids, 42, pp. 1995–2011 (1994).Google Scholar
31.Miehe, C. and Koch, A., “Computational Micro-To-Macro Transitions of Discretized Microstructures Undergoing Small Strains,” Archive of AppliedMechanics, 72, pp. 300–317 (2002).Google Scholar
32.Qin, Q. H. and Yang, Q. S., Macro-Micro Theory on Multifield Behaviour of Heterogeneous Materials, Higher Education Press & Springer, Beijing (2008).Google Scholar
33.Temizer, İ. and Wriggers, P., “An Adaptive Method for Homogenization in Orthotropic Nonlinear Elasticity,” Computer Methods in Applied Mechanics and Engineering, 196, pp. 3409–3423 (2007).Google Scholar
34.Sauter, S. A. and Schwab, C., Boundary Element Methods, Springer (2010).CrossRefGoogle Scholar
35.Rizzo, F. J. and Shippy, D. J., “A Method for Stress Determination in Plane Anisotropic Elastic Bodies,” Journal of Composite Materials, 4, pp. 36–61 (1970).Google Scholar
36.Wang, H. and Qin, Q. H., “Hybrid FEM with Fundamental Solutions as Trial Functions for Heat Conduction Simulation,” Acta Mechanica Solida Sinica, 22, pp. 487–498 (2009).Google Scholar
37.Qin, Q. H. and Wang, H., Matlab and C Programming for Trefftz Finite Element Methods, CRC Press, New York (2008).Google Scholar