Functionally graded material: A parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme

Computer Methods in Applied Mechanics and Engineering

Volumn 188, Issue 1, 2000, Pages 17-38

  Cho, J R ^a   Oden, J Tinsley ^b  

^a Pusan National University   (South Korea)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; MATHEMATICAL MODELS; OPTIMIZATION; STRESS ANALYSIS; THERMAL STRESS;

CRANK-NICOLSON-GALERKIN SCHEME; FUNCTIONALLY GRADED MATERIALS;

COMPOSITE MATERIALS;

EID: 0034229047     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00289-3     Document Type: Article

References (33)

1. A. Bedford M. Stern A multi-continuum theory for composite elastic materials Acta Mech. 14 1972 85 102
2. R.M. Bowen D.J. Garcia On the thermodynamics of mixtures with several temperatures Int. J. Engrg. Sci. 8 1970 63 83
3. B. Budiansky On the elastic moduli of some heterogeneous materials J. Mech. Phys. Solids 13 1965 223 227
4. D.S. Burnett Finite Element Analysis: From Concept to Applications 1988 Addison-Wesley Reading, MA
5. J.R. Cho J.T. Oden A priori modeling error estimates of hierarchical models for elasticity problems for plate- and shell-like structures Math. Comput. Modelling 23 10 1996 117 133
6. T. Chen G.J. Dvorak Y. Benveniste Mori–Tanaka estimates of the overall elastic moduli of certain composites J. Appl. Mech. 59 1992 539 546
7. R.M. Christensen Mechanics of Composite Materials 1979 Wiley/Interscience New York
8. A.E. Giannakopulos S. Suresh M. Olsson Elastoplastic analysis of thermal cycling: layered materials with compositional gradients Acta Metall. Mater. 43 4 1995 1335 1354
9. M. Grujicic Y. Zhang Determination of effective elastic properties of functionally graded materials using voronoi cell finite element method Mater. Sci. Engrg. A 251 1998 64 76
10. 3 multi-layered materials Mater. Sci. Engrg. A 205 1996 59 71
11. S. Ghosh S.N. Mukhopadhyay A material based finite element analysis of heterogeneous media involving dirichlet tessellations Comput. Meth. Appl. Mech. Engrg. 104 1993 221 247
12. Z. Hashin S. Shtrikman A variational approach to the theory of the elastic behavior of multiphase systems J. Mech. Phys. Solids 11 1963 127 140
13. R. Hill Elastic properties of reinforced solids: some theoretical principles J. Mech. Phys. Solids 11 1963 357 372
14. R. Hill Self-consistent mechanics of composite materials J. Mech. Phys. Solids 13 1965 213 222
15. C. Johnson Numerical Solution of Partial Differential Equations by the Finite Element Method 1990 Cambridge University Press Cambridge
16. 3 Acta Metall. Mater. 45 8 1997 3123 3134
17. M. Koizumi FGM activities in Japan Composites Part B 28B 1997 1 4
18. T. Mori K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metall. 21 1973 571 574
19. J.T. Oden, G.F. Carey, Finite Elements: Computational Aspects, vol. III, Prentice-Hall, Englewood Cliffs, NJ, 1984
20. J.T. Oden T. Zohdi Analysis and adaptive modeling of highly heterogeneous elastic structures Comput. Meth. Appl. Mech. Engrg. 148 1997 367 391
21. K.S. Ravichandran Elastic properties of two-phase composites J. Am. Ceram. Soc. 77 5 1994 1178 1184
22. T. Reiter G.J. Dvorak V. Tvergaard Micromechanical models for graded composite materials J. Phys. Solids 45 1997 1281 1302
23. T. Reiter G.J. Dvorak Micromechanical models for graded composite materials: II. Thermomechanical loading J. Phys. Solids 46 9 1998 1655 1673
24. R.A. Schapery Thermal expansion coefficients of composite materials J. Comput. Mater. 2 1968 380 404
25. S. Suresh A.E. Giannakopoulos M. Olson Elastoplastic analysis of thermal cycling: layered materials with sharp interfaces J. Mech. Phys. Solids 42 6 1994 978 1018
26. M. Takemura, A. Yoshitake, H. Hayakawa, T. Hyakubu, M. Tamura, Mechanical and thermal properties of FGM fabricated by thin lamination method, in: Proceedings of the First International Symposium on Functionally Gradient Materials Forum, 1990, pp. 97–100
27. Y. Tomota K. Kuroki T. Mori I. Tamura Tensile deformation of two-ductile-phase alloys: flow curves of α − γ Fe–Cr–Ni alloys Mater. Sci. Engrg. 24 1976 85 94
28. K. Wakashima H. Tsukamoto Mean-field micromechanics model and its application to the analysis of thermomechanical behavior of composite materials Mater. Sci. Engrg. A 146 1991 291 316
29. K. Wakashima H. Tsukamoto A unified micromechanical approach toward thermomechanical tailoring of metal matrix composites ISIJ Int. 32 8 1992 883 892
30. L.J. Walpole On the bounds for the overall elastic moduli of inhomogeneous systems J. Mech. Phys. Solids 14 1966 151 162
31. E. Weissenbek H.E. Pettermann S. Suresh Elasto-plastic deformation of compositionally graded metal–ceramic composites Acta Mater. 45 8 1997 3401 3417
32. R.L. Williamson B.H. Rabin J.T. Drake Finite element analysis of thermal residual stresses at graded ceramic–metal interfaces, Part 1, Model description and geometrical effects J. Appl. Phys. 74 2 1993 1310 1320
33. A. Yoshitake, M. Tamura, I. Shito, M. Niino, Fabrication of the functionally gradient materials (FGM), In: The State of Art, ESA Symposium on Space Applications of Advanced Structural Materials, 1990