Homogenization analysis for particulate composite materials using the boundary element method

CMES - Computer Modeling in Engineering and Sciences

Volumn 5, Issue 2, 2004, Pages 135-149

  Okada, Hiroshi ^a   Fukui, Yasuyoshi ^a   Kumazawa, Noriyoshi ^a  

^a KAGOSHIMA UNIVERSITY   (Japan)

Author keywords

Boundary element method (BEM); Ellipsoidal inclusion, eshelby's tensor; Homogenization method; Representative volume element (RVE)

Indexed keywords

BOUNDARY ELEMENT METHOD; ELASTIC MODULI; FINITE ELEMENT METHOD; INTEGRATION; STRESS CONCENTRATION; STRESSES; TENSORS;

ELLIPSOIDAL INCLUSION; ESHELBY'S TENSORS; HOMOGENIZATION METHOD; REPRESENTATIVE VOLUME ELEMENT (RVE);

COMPOSITE MATERIALS;

EID: 8344273540     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

1. Ashby, M. F.(1993): Criteria for selecting the components of composites, Acta Metall. Mater, vol. 41, pp. 1313-1335.
2. Atluri, S. N.; Han, Z. D.; Shen, S. (2003): Meshless Local Patrov-Galerkin (MLPG) approaches for weakly-singular traction & displacement boundary integral equations, CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. 5, pp. 507-517.
3. Banerjee, P.K.; Butterfield, R. B. (1981): Boundary Element Methods in Engineering and Science, McGraw-Hill, UK.
4. Banerjee, P.K.; Cathie, D.N. (1980): A direct formulation and numerical implementation of the boundary element method for two-dimensional problems of elastoplasticity, Int. J. Mech. Sci , vol. 22, pp. 233-245.
5. Banerjee, P.K.; Henry, D.P. (1992): Elastic analysis of three-dimensional solids with fiber inclusions by BEM, Int. J. of Solids Struct., vol. 29, pp. 2423-2440.
6. Banerjee, P.K.; Reveendra, S.T. (1987): New boundary element formulation for 2-D elastoplastic analysis, Journal of Engineering Mechanics, vol. 113, no. 2, pp. 252-265.
7. Bensoussan, A.; Lions, J.-L.; Papanicolaou, G. (1978): Aymptotic analysis for periodic structures, Studies in mathematics and its applications vol. 5, North-Holland, Amsterdam.
8. Chandra, A.; Mukherjee, S. (1983): Applications of the boundary element method to large strain large deformation problems of viscoplasticity, Journal of Strain Analysis, vol. 18, no. 4, pp. 261-270.
9. Chandra, A.; Mukherjee, S. (1986): An analysis of large strain viscoplasticity problems including the effects of induced material anisotropy, Journal of Applied Mechanics, vol. 53 pp. 77-82
10. Chung, P. W.; Namburu, R. R.; Henz, B. J. (2004): A Lattice Statics-Based Finite Element Method, CMES: Computer Modeling in Engineering & Sciences, Vol. 5, No. 1, pp. 45-62.
11. Cruse, T.A. (1969): Numerical solutions in three dimensional elastostatics, Int. J. of Solids Struct, vol. 5, pp. 1259-1274.
12. Eshelby, J.D. (1957): The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of Royal Society, London, vol. A24, pp. 376-396.
13. Fish, J. (1992): The S-Version of the Finite Element Method, Computers & Structures, vol. 43, pp. 539-547.
14. Fish, J., Guttal, R. (1996): The 5-Version of Finite Element Method for Laminated Composites, International Journal for Numerical Methods in Engineering, vol. 39, pp. 3641-3662.
15. Guedes, J. M.; Kikuchi, N. (1990): Preprocessing and postprocessing for Materials based on the homogenization method with adaptive finite element methods, Comput. Method Appl. Mech. Eng., Vol. 83, pp. 143-198.
16. Man, D. Z.; Atluri, S. N. (2003): On simple formulation of weakly singular traction & displacement BIE, and their solutions through Petrov-Galerkin Approaches, CMES: Computer Modeling in Engineering & Sciences, vol. 4, no. 1, pp. 5-20.
17. Higa, Y.; Tomita, Y. (2000): Modeling and Computational Simulation of Deformation Behavior of Particulate-Reinforced Composite Materials by Homogenization Method (in Japanese), Trans. JSME Series A, vol. 66, no. 648, pp. 1441-1446.
18. Hollister, S.J.; Kikuchi, N. (1992): A Comparison of homogenizetion and standard mechanics analyses for periodic porous composites, Comput. Mech., vol. 10, pp. 73-95.
19. Hollister, S.J.; Kikuchi, N. (1994): Homogenization theory and digital imaging: a basis for studying the mechanics and design principles of bone tissue, Biotechnology and Biongineering, vol. 43, pp. 586-596.
20. Kalamkarov, A. L. (1992): Composite and Reinforced Elements of Construction, John Wiley & Sons, Chich ester, England.
21. Kamiski, M. (1999): Boundary Element method homogenization of the periodic linear elastic fiber composites, Engineering Analysis with Boundary Elements, vol. 23, pp. 815-823.
22. Kane, J. H. (1994): Boundary Element Analysis in Engineering Continuum Mechanics, Prentice Hall, Engle-wood Cliffs, NJ.
23. Kato, T.; Nishioka, T. (2000): Analysis of Damaged Materials Containing Numerous Elliptical Cracks by Using the Homogenization Method (in Japanese), Trans. JSME Series A, vol. 66, no. 643, pp. 524-531.
24. Lee, K.; Moorthy, S.; Ghosh, S. (1999): Multiple scale computational model for damage in composite materials, Comput. Method Appl. Mech. Eng, vol. 172, pp. 175-201.
25. Moorthy, S.; Ghosh, S. (1998): A Voronoi cell finite element model for particle craking in elastic-plastic composite materials, Comput. Method Appl. Mech. Eng., vol. 151, pp. 377-400.
26. Mura, T. (1982): Mechanics of Defects in Solids, Martinus Nijhoff Publications, London.
27. Nishioka, T.; Kato, T. (1998): An alternating method based on the VNA solution for analysis of damaged solid containing arbitrarily distributed elliptical microcracks, International Journal of Fracture, vol. 89, pp. 159-192.
28. Ohno, N.; Matsuda, T.; Wu, X. (2001): A homogenization theory for elastic-viscoplastic composites with point symmetry of internal distributions, Int. J. of Solids Struct., vol. 38, pp. 2867-2878.
29. Ohno, N.; Wu, X.; Matsuda, T. (2000): Homogenized properties of elastic-viscoplastic composites with periodic internal structures, International Journal of Mechanical Sciences, vol. 42, pp. 1519-1536.
30. Ohno, N.; Okumura, D.; Noguchi, H. (2002): Microscopic Symmetric bifurcation condition of cellular soids based on a homogenization theory of finite defromation, Journal of the Mechanics and Physics of Solids, vol. 50, pp. 1125-1153.
31. Okada, H.; Atluri, S.N. (1994): Recent developments in the field-boundary element method for finite/small strain elastoplasticity, International Journal of Solids and Structures, vol. 31, pp. 1737-1775.
32. Okada, H.; Fujitani, S.; Fukui, Y.; Kumazawa, N. (2001): Analysis of Beam/Bar Structure based on Ho mogenization method (in Japanese), Trans JSME Series A, vol. 67, no. 658, pp. 933-939.
33. Okada, H.; Fukui, Y.; Kumazawa, N.; Maruyama, T. (1998): Homogenization Method for Nonlinear Materials undergoing Large Deformation (1st Report, Mathematical Formulations, Which can Rigorously Satisfy the Assumption of Periodicity) (in Japanese), Trans JSME Series A, vol. 64, no. 618, pp. 450-456.
34. Okada, H.; Fukui, Y.; Kumaszawa, N. (2000): Formulations for Homogenization Method Based on Boundary Element Method, Advances in Computational Engineering and Sciences Edt. by Brust and Atluri, pp. 1128-1133.
35. Okada, H.; Fukui, Y.; Kumazawa, N. (2001a): Homogenization method for heterogeneous material based on boundary element method, Comput. Struct., vol. 79, pp. 1987-2007.
36. Okada, H.; Fukui, Y.; Kumazawa, N. (2001b): A boundary element based meso-analysis on the evolution of material damage, in Advances in Fracture Research (Proceedings of ICF10 International Conference on Fracture) eds. K. Ravi-Chandar, B.L. Karihaloo, T. Kishi, R.O. Ritchie, A.T. Yokobori Jr., T. Yokobori, Pergamon (an imprint of Elsevier Science), CD-ROM.
37. Okada, H.; Fukui, Y.; Kumazawa, N. (2002): Homogenization Analysis using the Boundary Element Method (Formulations and Computer Implementation in Elastic Analysis) (in Japanese), Trans JSMA Series A, vol. 68, no. 666, pp. 181-188.
38. Okada, H.; Rajiyah, H.; Atluri, S.N. (1990): A full tangent stiffness field-boundary element formulation for geometric and material nonlinear problems of solid mechanics, International Journal for Numerical Methods in Engineering, vol. 29, pp. 15-35.
39. Okada, H.; Rajiyah, H.; Atluri, S.N. (1988): Some recent development in finite-strain elastoplasticity using the field-boundary element method, Computers & Structures vol. 30 (1/2), pp. 275-288.
40. Press, W.H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. (1996): Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, UK.
41. Procházka, P. (2001): Homogenization of linear and of debonding composites using BEM, Engineering Analysis with Boundary Elements, vol. 25, pp. 753-769.
42. Raghavan, P.; Ghosh, S. (2004): Adaptive Multi-scale Computational Modeling of Composite Materials, CMES: Computer Modeling in Engineering & Sciences, Vol. 5, No. 2, pp. 151-170.
43. Rizzo, F.J. (1967): An integral equation approach to boundary value problems of classical elastostatics, Quarterly of Applied Mathematics,vol. 25, pp. 83-95.
44. Shibuya, Y.; Wang, S.-S. (1994): Nonlinear Behavior of Metal Matrix Fiber Composites with Damage on Interface (in Japanese), Trans. JSME Series A, vol. 60, no. 569, pp. 153-158.
45. Silva, E.C.N.; Nishiwaki, S., Fonseca, J. S. O., Kikuchi, K. (1999): Optimization methods applied to material and Flextensional actuator design using the homogenization method, Comput. Method Appl. Mech. Eng, vol 172, pp. 241-271.
46. Takano, N.; Ohnishi, Y.; Zako, M.; Nishiyabu, K. (2000): The formulation of homogenization method applied to large deformation problem for composite materials, Int. J. of Solids Struct., vol. 37, pp. 6517-6535.
47. Takano, N.; Ohnishi, Y.; Zako, M.; Nishiyabu, K. (2001): Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization method, Int. J. of Solids Struct., vol. 38, pp. 6333-6352.
48. Takano, N.; Zako, M.; Kikuchi, N. (1995): Stress analysis of sandwich plate by the homogenization method, Materials Science Research International, vol. 1, no. 2, pp. 82-88.
49. Terada, K.; Hori, M.; Kyoya, T.; Kikuchi, N. (2000): Simulation of the multi-scale convergence in computational homogenization approaches, Int. J. of Solids Struct., vol. 37, pp. 2285-2311.
50. Terada, K.; Miura, T.; Kikuchi, N. (1997): Digital image-based modeling applied to the homogenization analysis of composite materials, Computational Mechanics, vol. 20, pp. 331-346.
51. Wienecke, H.A.; Brockenbrough, J.R.; Romanko, A.D. (1995): A Three-dimensional unit cell model with application toward particulate composites, Journal of Applied Mechanics, vol. 63, pp. 136-140.
52. Wu, X.; Ohno, N. (1999): A Homogenization Theory for time-dependent nonlinear composites with periodic internal structures, Int. J. of Solids Struct.,vol. 36, pp. 4991-5012.