This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions.
Issue Section:
Review Articles
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, and Hui
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,” Mater. Sci. Eng., A
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, and Lam
, K. Y.
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, T.
, and Sampath
, S.
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,” Functionally Graded Materials 2000, Proceedings of the Sixth International Symposium on Functionally Graded Materials
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, K.
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, I.
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, and S.
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, pp. 521
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.30.
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, Z.-H.
, 2002, “An Asymptotic Solution of Temperature Field in a Strip of a Functionally Graded Material
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, and Tanigawa
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, pp. 139
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, J.
, Sladek
, V.
, and Zhang
, Ch.
, 2003, “Transient Heat Conduction Analysis in Functionally Graded Materials by the Meshless Local Boundary Integral Equation Method
,” Comput. Mater. Sci.
0927-0256, 28
, pp. 494
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Chen
, J.
, Liu
, Z.
, and Zou
, Z.
, 2002, “Transient Internal Crack Problem for a Nonhomogeneous Orthotropic Strip (Mode I)
,” Int. J. Eng. Sci.
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, pp. 1761
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Chen
, B.
, and Tong
, L.
, 2004, “Sensitivity Analysis of Heat Conduction for Functionally Graded Materials
,” Mater. Des.
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, pp. 663
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Sutradhar
, A.
, and Paulino
, G. H.
, 2004, “The Simple Boundary Element Method for Transient Heat Conduction in Functionally Graded Materials
,” Comput. Methods Appl. Mech. Eng.
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, pp. 4511
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Sutradhar
, A.
, Paulino
, G. H.
, and Gray
, L. J.
, 2005, “On Hypersingular Surface Integral in the Symmetric Galerkin Boundary Element Method: Application to Heat Conduction in Exponentially Graded Materials
,” Int. J. Numer. Methods Eng.
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, pp. 122
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Sankar
, B. V.
, and Tzeng
, J. T.
, 2002, “Thermal Stresses in Functionally Graded Beams
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, pp. 1228
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Sankar
, B. V.
, 2001, “An Elasticity Solution for Functionally Graded Beams
,” Compos. Sci. Technol.
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, pp. 689
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.39.
Apetre
, N. A.
, Sankar
, B. V.
, and Ambur
, D. R.
, 2006, “Low-Velocity Impact of Sandwich Beams With Functionally Graded Core
,” Int. J. Solids Struct.
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Bhangale
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, and Ganesan
, N.
, 2006, “Thermoelastic Buckling and Vibration Behavior of a Functionally Graded Sandwich Beam With Constrained Viscoelastic Core
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, Pollien
, A.
, and Mortensen
, A.
, 2006, “Functional Grading of Metal Foam Cores for Yield-Limited Lightweight Sandwich Beams
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, A.
, Gopalakrishnan
, S.
, and Reddy
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, 2003, “A New Beam Finite Element for the Analysis of Functionally Graded Materials
,” Int. J. Mech. Sci.
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, pp. 519
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Chakraborty
, A.
, and Gopalakrishnan
, S.
, 2003, “A Spectrally Formulated Finite Element for Wave Propagation Analysis in Functionally Graded Beam
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, H. K.
, and Yen
, S. C.
, 2006, “Transient Thermoelastic Deformation of 2-D Functionally Graded Beams Under Nonuniformly Convective Heat Supply
,” Compos. Struct.
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, pp. 381
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Tsukamoto
, H.
, 2003, “Analytical Method of Inelastic Thermal Stresses in a Functionally Graded Material Plate by a Combination of Micro- and Macromechanical Approaches
,” Composites, Part B
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, pp. 561
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, and Tanigawa
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, 1999, “Three-Dimensional Transient Thermal Stresses of Functionally Graded Rectangular Plate Due to Partial Heating
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0149-5739, 22
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.47.
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, R. W.
, and Lutz
, M. P.
, 1999, “Thermal Stresses and Thermal Expansion in a Uniformly Heated Functionally Graded Cylinder
,” J. Therm. Stresses
0149-5739, 22
, pp. 178
–188
.48.
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, S.
, and Busso
, E. P.
, 2002, “Self-Consistent Elastoplastic Stress Solutions for Functionally Graded Material Systems Subjected to Thermal Gradients
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, pp. 695
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, J. N.
, 2000, “Analysis of Functionally Graded Plates
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, pp. 663
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, J. N.
, and Cheng
, Z.-Q.
, 2001, “Three-Dimensional Thermomechanical Deformations of Functionally Graded Rectangular Plates
,” Eur. J. Mech. A/Solids
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, pp. 841
–855
.51.
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, J. N.
, and Chen
, C. D.
, 1998, “Thermomechanical Analysis of Functionally Graded Cylinders and Plates
,” J. Therm. Stresses
0149-5739, 21
, pp. 593
–626
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, G. N.
, and Reddy
, J. N.
, 1998, “Nonlinear Transient Thermoelastic Analysis of Functionally Graded Ceramic-Metal Plates
,” Int. J. Solids Struct.
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, pp. 4457
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, C. T.
, Lam
, K. Y.
, and Reddy
, J. N.
, 1999, “Vibration of Functionally Graded Cylindrical Shells
,” Int. J. Mech. Sci.
0020-7403, 41
, pp. 309
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, G. N.
, Chin
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, and Reddy
, J. N.
, 1999, “Thermoelastic Analysis of Functionally Graded Ceramic-Metal Cylinder
,” J. Eng. Mech.
0733-9399, 125
, pp. 1259
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, S. C.
, Loy
, C. T.
, Lam
, K. Y.
, and Reddy
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, 2000, “Vibration Characteristics of Functionally Graded Cylindrical Shells Under Various Boundary Conditions
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, J. N.
, Wang
, C. M.
, and Kitipornchai
, S.
, 1999, “Axysimmetric Bending of Functionally Graded Circular and Annular Plates
,” Eur. J. Mech. A/Solids
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, pp. 185
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, and Batra
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, 2004, “Three Dimensional Exact Solution for the Vibration of Functionally Graded Rectangular Plates
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Vel
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, and Batra
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, and Batra
, R. C.
, 2004, “Transient Thermoelastic Deformations of a Thick Functionally Graded Plate
,” J. Therm. Stresses
0149-5739, 27
, pp. 705
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.60.
Qian
, L. F.
, Batra
, R. C.
, and Chen
, L. M.
, 2004, “Static and Dynamic Deformation of Thick Functionally Graded Elastic Plates by Using Higher-Order Shear and Normal Deformable Plate Theory and Meshless Local Petrov–Galerkin Method
,” Composites, Part B
1359-8368, 35
, pp. 685
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Kashtalyan
, M.
, 2004, “Three Dimensional Elasticity Solution for Bending of Functionally Graded Rectangular Plates
,” Eur. J. Mech. A/Solids
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, pp. 853
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.62.
Elishakoff
, I.
, and Gentilini
, C.
, 2005, “Three-Dimensional Flexure of Rectangular Plates Made of Functionally Graded Materials
,” ASME J. Appl. Mech.
0021-8936, 72
, pp. 788
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.63.
Pan
, E.
, 2003, “Exact Solution for Functionally Graded Anisotropic Elastic Composite Laminates
,” J. Compos. Mater.
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, pp. 1903
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Soldatos
, K. P.
, 2004, “Complex Potential Formalisms for Bending of Inhomogeneous Monoclinic Plates Including Transverse Shear Deformations
,” J. Mech. Phys. Solids
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, L. D.
, and Venini
, P.
, 2004, “Finite Elements for Functionally Graded Reissner-Mindlin Plates
,” Comput. Methods Appl. Mech. Eng.
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Bilgili
, E.
, Bernstein
, B.
, and Arastoopour
, H.
, 2003, “Effect of Material Non-Homogeneity on the Inhomogeneous Shearing Deformations of a Gent Slab Subjected to a Temperature Gradient
,” Int. J. Non-Linear Mech.
0020-7462, 38
, pp. 1351
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Cheng
, Z.-Q.
, 2001, “Nonlinear Bending of Inhomogeneous Plates
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0141-0296, 23
, pp. 1359
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Ramirez
, F.
, Heyliger
, P. R.
, and Pan
, E.
, 2005, “Static Analysis of Functionally Graded Elastic Anisotropic Plates Using a Discrete Layer Approach
,” Composites, Part B
1359-8368, 37
, pp. 10
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.69.
Na
, K.-S.
, and Kim
, J.-H.
, 2006, “Nonlinear Bending Response of Functionally Graded Plates Under Thermal Loads
,” J. Therm. Stresses
0149-5739, 29
, pp. 245
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Chi
, S.-H.
, and Chung
, Y.-L.
, 2006, “Mechanical Behavior of Functionally Graded Material Under Transverse Load—Part I: Analysis
,” Int. J. Solids Struct.
0020-7683, 43
, pp. 3657
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Chi
, S.-H.
, and Chung
, Y.-L.
, 2006, “Mechanical Behavior of Functionally Graded Material Under Transverse Load—Part II: Numerical Results
,” Int. J. Solids Struct.
0020-7683, 43
, pp. 3675
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Yang
, J.
, Liew
, K. M.
, and Kitipornchai
, S.
, 2006, “Stochastic Analysis of Computationally Graded Plates With System Randomness Under Static Loading
,” Int. J. Solids Struct.
0020-7683, 47
, pp. 1519
–1541
.73.
Zenkour
, A. M.
, 2005, “A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 1—Deflections and Stresses
,” Int. J. Solids Struct.
0020-7683, 42
, pp. 5224
–5242
.74.
Zenkour
, A. M.
, 2005, “A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 2—Buckling and Free Vibration
,” Int. J. Solids Struct.
0020-7683, 42
, pp. 5243
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.75.
Woo
, J.
, and Meguid
, S. A.
, 2001, “Nonlinear Analysis of Functionally Graded Plates and Shallow Shells
,” Int. J. Solids Struct.
0020-7683, 38
, pp. 7409
–7421
.76.
Liew
, K. M.
, Kitipornchai
, S.
, Zhang
, X. Z.
, and Lim
, C. W.
, 2003, “Analysis of the Thermal Stress Behaviour of Functionally Graded Hollow Circular Cylinders
,” Int. J. Solids Struct.
0020-7683, 40
, pp. 2355
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.77.
Jabbari
, M.
, Sohrabpor
, S.
, and Eslami
, M. R.
, 2002, “Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads
,” Int. J. Pressure Vessels Piping
0308-0161, 79
, pp. 493
–497
.78.
Tarn
, J.-Q.
, 2001, “Exact Solutions for Functionally Graded Anisotropic Cylinders Subjected to Thermal and Mechanical Loads
,” Int. J. Solids Struct.
0020-7683, 38
, pp. 8189
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.79.
Tutuncu
, N.
, and Ozturk
, M.
, 2001, “Exact Solutions for Stresses in Functionally Graded Pressure Vessels
,” Composites, Part B
1359-8368, 32
, pp. 683
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.80.
Ruhi
, M.
, Angoshtari
, A.
, and Naghdabadi
, R.
, 2005, “Thermoelastic Analysis of Thick-Walled Finite-Length Cylinders of Functionally Graded Materials
,” J. Therm. Stresses
0149-5739, 28
, pp. 391
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.81.
Shao
, Z. S.
, and Wang
, T. J.
, 2006, “Three-Dimensional Solutions for the Stress Fields in Functionally Graded Cylindrical Panel with Finite Length and Subjected to Thermal/Mechanical Loads
,” Int. J. Solids Struct.
0020-7683, 43
, pp. 3856
–3874
.82.
Pelletier
, J. L.
, and Vel
, S. S.
, 2006, “An Exact Solution for the Steady-State Thermoelastic Response of Functionally Graded Orthotropic Cylindrical Shells
,” Int. J. Solids Struct.
0020-7683, 43
, pp. 1131
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.83.
Eraslan
, A. N.
, and Akis
, T.
, 2006, “On the Plane Strain and Plane Stress Solutions of Functionally Graded Rotating Solid Shaft and Solid Disk Problems
,” Acta Mech.
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, pp. 43
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Javaheri
, R.
, and Eslami
, M. R.
, 2002, “Thermoelastic Buckling of Rectangular Plates Made of Functionally Graded Materials
,” AIAA J.
0001-1452, 40
, pp. 162
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Javaheri
, R.
, and Eslami
, M. R.
, 2002, “Buckling of Functionally Graded Plates Under In-Plane Compressive Loading
,” ZAMM
0044-2267, 82
, pp. 277
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.86.
Javaheri
, R.
, and Eslami
, M. R.
, 2002, “Thermal Buckling of Functionally Graded Plates Based on Higher-Order Theory
,” J. Therm. Stresses
0149-5739, 25
, pp. 603
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Na
, K.-S.
, and Kim
, J.-H.
, 2004, “Three-Dimensional Thermal Buckling Analysis of Functionally Graded Materials
,” Composites, Part B
1359-8368, 35
, pp. 429
–437
.88.
Na
, K.-S.
, and Kim
, J.-H.
, 2006, “Three-Dimensional Thermomechanical Buckling Analysis for Functionally Graded Composite Plates
,” Compos. Struct.
0263-8223, 73
, pp. 413
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.89.
Na
, K.-S.
, and Kim
, J.-H.
, 2006, “Thermal Postbuckling Investigations of Functionally Graded Plates Using 3-D Finite Element Method
,” Finite Elem. Anal. Design
0168-874X, 42
, pp. 749
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.90.
Ganapathi
, M.
, and Prakash
, T.
, 2006, “Thermal Buckling of Simply Supported Functionally Graded Skew Plates
,” Compos. Struct.
0263-8223, 74
, pp. 247
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.91.
Yang
, J.
, Liew
, K. M.
, and Kitipornchai
, S.
, 2005, “Second-Order Statistics of the Elastic Buckling of Functionally Graded Rectangular Plates
,” Compos. Sci. Technol.
0266-3538, 65
, pp. 1165
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.92.
Najafizadeh
, M. M.
, and Eslami
, M. R.
, 2002, “First-Order-Theory Based Thermoelastic Stability of Functionally Graded Material Circular Plates
,” AIAA J.
0001-1452, 40
, pp. 1444
–1450
.93.
Najafizadeh
, M. M.
, and Eslami
, M. R.
, 2002, “Buckling Analysis of Circular Plates of Functionally Graded Material Under Uniform Radial Compression
,” Int. J. Mech. Sci.
0020-7403, 44
, pp. 2479
–2493
.94.
Ma
, L. S.
, and Wang
, T. J.
, 2004, “Relationships Between Axisymmetric Bending and Buckling Solutions of, FGM Circular Plates Based on Third-Order and Classical Plate Theories
,” Int. J. Solids Struct.
0020-7683, 41
, pp. 85
–101
.95.
Chen
, X. L.
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.Copyright © 2007
by American Society of Mechanical Engineers
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