Analysis of composite materials: A survey

Journal of Applied Mechanics, Transactions ASME

Volumn 50, Issue 3, 1983, Pages 481-505

  Hashin, Z ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTICITY; MECHANICS; VISCOELASTICITY;

COMPOSITE MATERIALS;

EID: 0020816026     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3167081     Document Type: Article

References (177)

1. Hashin, Z., Theory of Fiber Reinforced Materials, NASA CR-1974, 1972.
2. Christensen, R. M., Mechanics of Composite Materials, Wiley-Interscience, New York, 1979.
3. Hashin, Z., “Theory of Mechanical Behavior of Heterogeneous Media,” Applied Mechanics Reviews, Vol. 17, 1964, pp. 1-9.
4. Beran, M. J., Statistical Continuum Theories, Wiley, New York, 1968.
5. Einstein, A., “Eine Neue Bestimmung der Molekiildimensionen,” Annalen der Physik, Vol. 19, 1906, pp. 289-306, Vol. 34, 1911, pp. 591-592 (errata). English translation in Investigations on the Theory of Brownian Motion, Dover, 1956, pp. 36-62.
6. Hill, R., “Elastic Properties of Reinforced Solids: Some Theoretical Principles,” Journal of the Mechanics and Physics of Solids, Vol. 11, 1963, pp. 357-372.
7. Herrmann, G., in an oral presentation in 1967 of Herrmann, G., and Achenbach, J. D., “Wave Propagation in Laminated and Fiber-Reinforced Composites,” in Mechanics of Composite Materials, Pergamon Press, 1970, pp. 337-360.
8. Beran, M. J., and McCoy, J. J., “Mean Field Variations in a Statistical Sample of Heterogeneous Linearly Elastic Solids,” International Journal of Solids and Structures, Vol. 6, 1970, pp. 1035-1054.
9. Levin, V. M., “The Relation Between Mathematical Expectation of Stress and Strain Tensors in Elastic Microheterogeneous Media,” Prikladnaya Matematika y Mekhanika (English translation from Russian), Vol. 35, 1971, pp. 694-701.
10. Beran, M. J., “Application of Statistical Theories for the Determination of Thermal, Electrical and Magnetic Properties of Heterogeneous Materials,” in Composite Materials, Vol. 2, Sendeckyj, G. P., ed., Academic Press, New York, 1974, pp. 209-249.
11. Eshelby, J. D., “The Determination of the Field of an Ellipsoidal Inclusion and Related Problems,” Proceedings of the Royal Society, London, Vol A, No. 241, 1957, pp. 376-396.
12. Dewey, J. M., “The Elastic Constants of Materials Loaded With Non-rigid Fillers,” Journal of Applied Physics, Vol. 18, 1947, pp. 578-581.
13. Hashin, Z., “The Moduli of an Elastic Solid Containing Spherical Particles of Another Elastic Material,” in Nonhomogeneity in Elasticity and Plasticity, Olszak, W. ed., Pergamon Press, 1959, pp. 463-478.
14. Chen, H. S., and Acrivos, A., “The Effective Elastic Moduli of Composite Materials Containing Spherical Particles at Non-Dilute Concentrations,” International Journal of Solids and Structures, Vol. 14, 1978, pp. 349-364.
15. Batchelor, G. K., and Green, J. T., “The Determination of the Bulk Stress in a Suspension of Spherical Particles to Order c2,” Journal of Fluid Mechanics, Vol. 56, 1972, pp. 401-427.
16. Hashin, Z., “The Elastic Moduli of Heterogeneous Materials,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 29, 1962, pp. 143-150.
17. Lee, K. J., and Westmann, R. A., “Elastic Properties of Hollow-Sphere-Reinforced Composites,” Journal of Composite Materials, Vol. 4, 1970, pp. 242-253.
18. Molyneux, J., and Beran, M. J., “Statistical Properties of the Stress and Strain Fields in a Medium With Small Random Variations in Elastic Coefficients,” Journal of Mathematics and Mechanics, Vol. 14, 1965, pp. 337-352.
19. Paul, B., “Prediction of Elastic Constants of Multiphase Materials,” Transactions ofthe ASME, Vol. 218, 1960, pp. 36-41.
20. Hashin, Z., and Shtrikman, S., “A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials,” Journal of the Mechanics and Physics of Solids, Vol. 11, 1963, pp. 127-140.
21. Hashin, Z., and Shtrikman, S., “On Some Variational Principles in Anisotropic and Nonhomogeneous and Elasticity,” Journal of the Mechanics and Physics of Solids, Vol. 10, 1962, pp. 335-342.
22. Hashin, Z., “On Elastic Behaviour of Fibre Reinforced Materials of Arbitrary Transverse Phase Geometry,” Journal of Mechanics and Physics of Solids, Vol. 13, 1965, pp. 119-134.
23. Walpole, L. J., “On Bounds for the Overall Elastic Moduli of Inhomogeneous Systems-I,” Journal of the Mechanics and Physics of Solids, Vol. 14, 1966, pp. 151-162.
24. Hill, R., “New Derivations of Some Elastic Extremum Principles,” in Progress in Applied Mechanics, Prager Anniversary Volume, Macmillan, New York, 1963, pp. 91-106.
25. Korringa, J., “Theory of Elastic Constants of Heterogeneous Media,” Journal of Mathematics and Physics, Vol. 14, 1973, pp. 509-513.
26. Willis, J. R., “Bounds and Self-Consistent Estimates for the Overall Moduli of Anisotropic Composites,” Journal of the Mechanics and Physics of Solids, Vol. 25, 1977, pp. 185-202.
27. Willis, J. R., “Variational and Related Methods for the Overall Properties of Composites,” in Advances in Applied Mechanics, Vol. 21, Yih, C.S., ed., Academic Press, New York, 1981, pp. 1-78.
28. Kroner, E., “Bounds for Effective Elastic Moduli of Disordered Materials,” Journal of the Mechanics and Physics of Solids, Vol. 25, 1977, pp. 137-155.
29. Wu, C. T. D., and McCullough, R. L., “Constitutive Relationships for Heterogeneous Materials,” in Developments in Composite Materials, Holister, G. S., ed., 1977, pp. 119-187.
30. Watt, P. J., and O’Connell, R. J., “An Experimental Investigation of the Hashin-Shtrikman Bounds on Two-Phase Aggregate Elastic Properties,” Physics of the Earth and Planetary Interiors, Vol. 21, 1980, pp. 359-370.
31. McCoy, J. J., “Macroscopic Response of Continua With Random Microstructures,” in Mechanics Today, Vol. 6, Nemat-Nasser, S., ed., Pergamon Press, 1981, pp. 1-40.
32. Milton, G. W., “Bounds on the Elastic and Transport Properties of Two-Component Composites,” Journal of the Mechanics and Physics of Solids, Vol. 30, 1982, pp. 177-191.
33. Sendeckyj, G. P., “Elastic Behavior of Composites,” in Composite Materials, Vol. 2, Sendeckyj, G. P., ed., Academic Press, New York, 1974, pp. 45-83.
34. Kroner, E., “Elastic Moduli of Perfectly Disordered Materials,” Journal of the Mechanics and Physics of Solids, Vol. 15, 1967, pp. 319-329.
35. Budiansky, B., “On the Elastic Moduli of Some Heterogeneous Materials,” Journal of the Mechanics and Physics of Solids, Vol. 13, 1965, pp. 223-227.
36. Hill, R., “A Self Consistent Mechanics of Composite Materials,” Journal of the Mechanics and Physics of Solids, Vol. 13, 1965, pp. 213-222.
37. Wu, T. T., “The Effect of Inclusion Shape on the Elastic Moduli of a Two-Phase Material,” International Journal of Solids and Structures, Vol. 2, 1966, pp. 1-8.
38. Kerner, E. H., “The Elastic and Thermoelastic Properties of Composite Media,” Proceedings of the Physical Society, Vol. B69, 1956, pp. 807-808.
39. Van der Poel, C., “On the Rheology of Concentrated Suspensions,” RheologicaActa, Vol. 1, 1958, pp. 198-205.
40. Smith, J. C., “Correction and Extension of Van der Poel’s Method for Calculating the Shear Modulus of a Particulate Composite,” Journal of Research of the National Bureau of Standards, Vol. 78, 4, 1974, pp. 355-362.
41. Christensen, R. M., and Lo, K. H., “Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,” Journal of the Mechanics and Physics of Solids, Vol. 27, 1979, pp. 315-330.
42. Hashin, Z., “Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites,” Journal of Composite Materials, Vol. 2, 1968, pp. 284-300.
43. Boucher, S., “On the Effective Moduli of Isotropic Two-Phase Elastic Composites,” Journal of Composite Materials, Vol. 8, 1974, pp. 82-89.
44. Mclaughlin, R., “A Study of the Differential Scheme for Composite Materials,” International Journal of Engineering Science, Vol. 15, 1977, pp. 237-244.
45. Christensen, R. M., and Waals, F. M., “Effective Stiffness of Randomly Oriented Fiber-Reinforced Composites,” Journal of Composite Materials, Vol. 6, 1972, pp. 518-532.
46. Voigt, W., Lehrbuch der Kristallphysik, Teubner, Berlin, 1910.
47. Reuss, A., “Berechnung der Fliessgrense von Mischkristallen auf Grund der Plastizitatsbedingung für Einkristalle,” Zeitschrift für Angewandte Mathematik andMechanik, Vol. 9, 1929, pp. 49-58.
48. Hill, R., “The Elastic Behaviour of a Crystalline Aggregate,” Proceedings of the Physical Society, London, Vol. 465, 1952, pp. 349-354.
49. Hashin, Z., and Shtrikman, S., “A Variational Approach to the Theory of the Elastic Behaviour of Polycrystals,” Journal of the Mechanics and Physics of Solids, Vol. 10, 1962, pp. 343-352.
50. Peselnick, L., and Meister, R., “Variational Method for Determining Effective Moduli of Polycrystals: (A) Hexagonal Symmetry, (B) Trigonal Symmetry,” Journal of Applied Physics, Vol. 36, 1965, pp. 2879-2884; also, Vol. 37, 1966, pp. 4121-4125.
51. Watt, P. J., “Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals With Orthorhombic Symmetry,” Journal of Applied Physics, Vol. 50, 1979, pp. 6290-6295; “… with Monoclinic Symmetry,” Vol. 51, 1980, pp. 1520-1524.
52. Watt, P. J., and Peselnick, L., “Clarification of the Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals With Hexagonal, Trigonal and Tetragonal Symmetries,” Journal of Applied Physics, Vol. 51, 1980, pp. 1525-1531.
53. Hashin, Z., “Elasticity of Random Media,” Transactions of the Society of Rheology, Vol. 9, 1965, pp. 381-406.
54. Walpole, L. J., “On Bounds for the Overall Elastic Moduli of Inhomogeneous Systems-II,” Journal of the Mechanics and Physics of Solids, Vol. 14, 1966, pp. 289-301.
55. Hershey, A. V., “The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 21, 1954, pp. 236-240.
56. Kroner, E., “Berechnung der Elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls,” Zeitschrift für Physik, Vol. 151, 1958, pp. 504-518.
57. Hill, R., “Theory of Mechanical Properties of Fibre-Strengthened Materials-I. Elastic Behaviour,” Journal of the Mechanics and Physics of Solids, Vol. 12, 1964, pp. 199-212.
58. Hashin, Z., and Rosen, B. W., “The Elastic Moduli of Fiber-Reinforced Materials,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 31, 1964, pp. 223-232.
59. Pickett, G., and Johnson, M. W., “Analytical Procedures for Predicting the Mechanical Properties of Fiber Reinforced Composites,” AFML-TR-65-2200, Air Force Materials Laboratory, Wright Patterson AFB, 1965.
60. Adams, D. F., Doner, D. R., and Thomas, R. L., “Mechanical Behavior of Fiber Reinforced Composite Materials,” AFML-TR-67-96, Air Force Materials Laboratory, Wright-Patterson AFB, 1967 (See also Journal of Composite Materials, Vol. 1, 1967, pp. 4-17, pp. 152-165.
61. Chen, C. H., and Cheng, S., “Mechanical Properties of Fiber Reinforced Composites,” Journal of Composite Materials, Vol. 1, 1967, pp. 30-41.
62. Love, A. E. H., A Mathematical Treatise on the Theory of Elasticity, Dover, 1944.
63. Hashin, Z., “Analysis of Properties of Fiber Composites With Anisotropic Constituents,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 46, 1979, pp. 543-550.
64. Hill, R., “Theory of Mechanical Properties of Fibre-Strengthened Materials-III. Self-Consistent Model,” Journal of the Mechanics and Physics of Solids, Vol. 13, 1965, pp. 189-198.
65. Chu, T. W., Nomura, S., and Taya, M., “A Self Consistent Approach to the Elastic Stiffness of Short-Fiber Composites,” Journal of Composite Materials, Vol. 14, 1980, pp. 178-188.
66. Hermans, J. J., “The Elastic Properties of Fiber Reinforced Materials When the Fibers are Aligned,” Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, Series B, Vol. 70, 1967, pp. 1-9.
67. Ashton, J. E., Halpin, J. C., and Petit, P. H., Primer on Composite Materials, Chapter 5, Technomic, 1969.
68. Bristow, J. R., “Microcracks and the Static and Dynamic Elastic Constants of Annealed and Heavily Cold-Worked Metals,” British Journal of Applied Physics, Vol. 11, 1960, pp. 81-85.
69. Walsh, J. B., “The Effect of Cracks on the Compressibility of Rock,” Journal of Geophysical Research, Vol. 70, 1965, pp. 381-389, “The Effect of Cracks on the Uniaxial Elastic Compression of Rocks,” pp. 399-411. “The Effect of Cracks in Rocks on Poisson’s Ratio,” pp. 5249-5257.
70. Piau, M., “Crack Induced Anisotropy and Scattering in Stressed Rocks: Effective Moduli and Attenuation,” International Journal of Engineering Science, Vol. 18, 1980, pp. 549-568.
71. Gottesman, T., “Effective Elastic Moduli of Cracked Materials,” Ph.D. Dissertation, Tel-Aviv University, 1980.
72. Gottesman, T., Hashin, Z., and Brull, M. A., “Effective Elastic Moduli of Cracked Fiber Composites,” in Advances in Composite Materials, Proc. ICCM3, Bunsell et al. eds., Pergamon Press, 1980, pp. 749-758.
73. Delameter, W. R., Herrmann G., and Barnett, D. M., “Weakening of an Elastic Solid by a Rectangular Array of Cracks,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 42, 1975, pp. 74-80, Erratum, Vol. 44, 1977, p. 190.
74. Budiansky, B., and O’Connell, R. J., “Elastic Moduli of a Cracked Solid,” International Journal of Solids and Structures, Vol. 12, 1976, pp. 81-97.
75. Hoenig, A., “Elastic Moduli of a Non-Randomly Cracked Body,” International Journal of Solids and Structures, Vol. 15, 1979, pp. 137-154.
76. Hashin, Z., and Derby, E. A., “Evaluation of the Non-Linear Stress Strain Behavior of Sheet Molding Compounds,” TFR 6301/1010. 1979, Materials Sciences Corp.
77. Willis, J. R., “A Polarization Approach to the Scattering of Elastic Waves. II. Multiple Scattering from Inclusions,” Journal of Mechanics and Physics of Solids, Vol. 28, 1980, pp. 307-327.
78. Walpole, L. J., “Elastic Behaviour of Composite Materials: Theoretical Foundations,” in Advances in Applied Mechanics, Vol. 21, Yih, C. S., ed., Academic Press, New York, 1981, pp. 169-242.
79. Levin, V. M., “On the Coefficients of Thermal Expansion of Heterogeneous Materials,” Mekhanika Tverdogo Tela, Vol. 1, 1967, pp. 88-94, English translation-Mechanics of Solids, Vol. 2, 1967, pp. 58-61.
80. Rosen, B. W., “Thermal Expansion Coefficients of Composite Materials, “Ph.D. Dissertation, University of Pennsylvania, 1968.
81. Schapery, R. A., “Thermal Expansion Coefficients of Composite Materials Based on Energy Principles,” Journal of Composite Materials, Vol. 2, 1968, pp. 380-404.
82. Rosen, B. W., and Hashin, Z., “Effective Thermal Expansion Coefficients and Specific Heats of Composite Materials,” International Journal of Engineering Science, Vol. 8, 1970, pp. 157-173.
83. Schapery, R. A., “Viscoelastic Behavior and Analysis of Composite Materials,” in Composite Materials, Vol. 2, Sendeckyj, G. P., ed., Academic Press, New York, 1974, pp. 84-168.
84. Hashin, Z., “Viscoelastic Behavior of Heterogeneous Media,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 32, 1965, pp. 630-636.
85. Hashin, Z., “Viscoelastic Fiber Reinforced Materials,” AIAA Journal, Vol. 4, 1966, pp. 1411-1417.
86. Christensen, R. M., Theory of Viscoelasticity, Academic Press, New York, 1971.
87. Hashin, Z., “Complex Moduli of Viscoelastic Composites: I. General Theory and Application to Participate Composites,” International Journal of Solids and Structures, Vol. 6, 1970, pp. 539-552. “II. Fiber Reinforced Materials,” ibid., Vol. 6, 1970, pp. 797-807.
88. Christensen, R. M., “Viscoelastic Properties of Heterogeneous Media,” Journal of the Mechanics and Physics of Solids, Vol. 17, 1969, pp. 23-41.
89. Roscoe, R., “Bounds for the Real and Imaginary Parts of the Dynamic Moduli of Composite Viscoelastic System,” Journal of the Mechanics and Physics of Solids, Vol. 17, 1969, 17-22.
90. Roscoe, R., “Improved Bounds for Real and Imaginary Parts of Complex Moduli of Isotropic Viscoelastic Composites,” Journal of the Mechanics and Physics of Solids, Vol. 20, 1972, pp. 91-99.
91. Laws, N., and McLaughlin, R., “Self-Consistent Estimates for the Viscoelastic Creep Compliances of Composite Materials,” Proceedings of the Royal Society, London, Series, A, Vol. 359, pp. 251-273.
92. Maxwell, J. C., Treatise on Electricity and Magnetism, 1st Ed., Clarendon Press, Oxford, 1873, p. 365.
93. Boettcher, C. J. F., Theory of Electric Polarization, Elsevier, 1952.
94. Jeffrey, D. J., “Conduction Through a Random Suspension of Spheres,” Proceedings of the Royal Society, London, Series A, Vol. 335, 1973, pp. 355-367.
95. McCoy, J. J., and Beran, M. J., “On the Effective Thermal Conductivity of a Random Suspension of Spheres,” International Journal of Engineering Science, Vol. 104, 1976, pp. 7-18.
96. Hashin, Z., and Shtrikman, S., “A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials,” Journal of Applied Physics, Vol. 33, 1962, pp. 1514-1517.
97. Lord Rayleigh, “On the Influence of Obstacles Arranged in Rectangular Order Upon the Properties of a Medium,” Philosophical Magazine, Vol. 34, 1892, pp. 481-502.
98. Meredith, R. E., and Tobias, C. W., “Resistance to Potential Flow Through a Cubical Array of Spheres,” Journal of Applied Physics, Vol. 31, 1960, pp. 1270-1275.
99. McPhedran, R. C., and McKenzie, D. R., “The Conductivity of Lattices of Spheres. I. The Simple Cubic Lattice,” Proceedings of the Royal Society, London, Series A, Vol. 359, 1978, pp. 45-63.
100. Bergman, D. J., “The Dielectric Constant of a Simple Cubic Array of Spheres,” Journal of Applied Physics, Vol. C12, 1979, pp. 4947
101. Hashin, Z., “Rapporteurs Report,” Proceedings of the 1975 International Conference on Composite Materials, Metallurgical Society of AIME, 1976, pp. 472-483.
102. Brown, W. F., “Solid Mixture Permittivities,” Journal of Chemical Physics, Vol. 23, 1955, pp. 1514-1517.
103. Beran, M. J., and Molyneux, J., “Statistical Properties of the Electric Field in a Medium With Small Random Variations in Permittivity,” II Nuovo Cimento, Vol. 30, 1963, pp. 1406-1422.
104. Beran, M. J., “Application of Statistical Theories for the Determination of Thermal, Electrical and Magnetic Properties of Heterogeneous Materials,” in Mechanics of Composite Materials, Vol. 2, of Composite Materials, Academic Press, New York, 1974, pp. 209-249.
105. Wiener, O., Abhandlungen der Mathematisch-Physischen Klasse der Königlichen Sächsischen Gesellschaft der Wissenschaften, Vol. 32, 1912, p. 509.
106. Bergman, D. J., “The Dielectric Constant of a Composite Material-A Problem in Classical Physics,” Physics Reports (Section C of Physics Letters), Vol. 43, 1978, pp. 377-407.
107. Prager, S., “Improved Variational Bounds on Some Bulk Properties of a Two-Phase, Random Medium,” Journal of Chemical Physics, Vol. 50, 1969, pp. 4305-4312.
108. Landauer, R., “Electrical Conductivity in Inhomogeneous Media,” in Electrical, Transport and Optical Properties of Inhomogeneous Media, American Institute of Physics, 1978, pp. 2-43.
109. Springer, G. S., and Tsai, S. W., “Thermal Conductivities of Unidirectional Materials,” Journal of Composite Materials, Vol. 1, 1967, pp. 166-173.
110. Hashin, Z., “Theory of Composite Materials,” in Mechanics of Composite Materials, Pergamon Press, 1970, pp. 201-242.
111. Keller, J. B., “A Theorem on the Conductivity of a Composite Medium,” Journal of Mathematical Physics, Vol. 5, 1964, pp. 548-549.
112. Mendelson, K. S., “A Theorem on the Conductivity of Two-Dimensional Heterogeneous Medium,” Journal of Applied Physics, Vol. 46, 1975, pp. 917-918.
113. Beran, M. J., and Silnutzer, N., “Effective Electrical, Thermal and Magnetic Properties of Fiber Reinforced Materials,” Journal of Composite Materials, Vol. 5, 1971, pp. 246-249.
114. Hori, M., and Yonezawa, F., “Statistical Theory of Effective Electrical, Thermal and Magnetic Properties of Random Heterogeneous Materials. V. One and Two-Dimensional Systems,” Journal of Mathematical Physics, Vol. 16, 1975, pp. 365-377.
115. Schulgasser, K., “On the Conductivity of Fiber Reinforced Materials,” Journal of Mathematical Physics, Vol. 17, 1976, pp. 382-387.
116. Schulgasser, K., “Concerning the Effective Transverse Conductivity of a Two-Dimensional Two-Phase Material,” International Journal of Heat and Mass Transfer, Vol. 20, 1977, pp. 1273-1280.
117. Schulgasser, K., and Hashin, Z., “Bounds for Effective Permittivities of Lossy Dielectric Composites,” Journal of Applied Physics, Vol. 47, 1975, pp. 424-427.
118. Milton, G. W., “Bounds on the Complex Dielectric Constant of a Composite Material,” Applied Physics Letters, Vol. 37, 1980, pp. 300-302.
119. Bergman, D. J., “Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material,” Physical Review Letters, Vol. 44, 1980, pp. 1285-1287.
120. Bruggeman, D. A. G., “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen,” Annalen der Physik, Vol. 24, 1935, pp. 636-679.
121. Landauer, R., “Electrical Resistance of Binary Mixtures,” Journal of Applied Physics, Vol. 23, 1952, pp. 779-784.
122. Kerner, E. H., “The Electrical Conductivity of Composite Media,” Proceedings of the Physical Society, Vol. 569, 1956, pp. 802-807.
123. Paul, B., “Macroscopic Criteria for Plastic Flow and Brittle Fracture,” in Fracture, Liebowitz, H., ed., Vol. III, Chapter 4, Academic Press, New York, 1968.
124. Drucker, D. C., “On Minimum Weight Design and Strength of Nonhomogeneous Plastic Bodies,” in Nonhomogeneity in Elasticity and Plasticity, Olszak, W., ed., Pergamon Press, 1959, pp. 139
125. Kelly, A., Strong Solids, Clarendon Press, Oxford, 1966.
126. Rosen, B. W., “Tensile Failure of Fibrous Composites,” Journal of the AIAA, Vol. 2, 1964, pp. 1985-1991.
127. Zweben, C., and Rosen, B. W., “A Statistical Theory of Material Strength With Application to Composite Materials,” Journal of the Mechanics and Physics of Solids, Vol. 18, 1970, pp. 180-206.
128. Rosen, B. W., and Zweben, C. H., “Tensile Failure Criteria for Fiber Composite Materials,” NASA CR-2057, Aug. 1972.
129. Hedgepeth, J. M., and Van Dyke, P., “Local Stress Concentrations in Imperfect Filamentary Composite Materials,” Journal of Composite Materials, Vol. 1, 1967, pp. 294-309.
130. Harlow, D. G., and Phoenix, S. L., “The Chain-of-Bundles Probability Model for the Strength of Fibrous Materials, I. Analysis and Conjectures,” Journal of Composite Materials, Vol. 12, 1978, pp. 195-214. “II. A Numerical Study of Convergence, “ibid, Vol. 12, 1978, pp. 314-334.
131. Phoenix, S. L., “Statistical Aspects of Failure of Fibrous Materials,” in Composite Materials: Testing and Design, STP674 ASTM, 1979, pp. 455-483.
132. Rosen, B. W., “Mechanics of Composite Strengthening,” in Fiber Composite Materials, American Society for Metals, 1965.
133. Schuerch, H., “Prediction of Compressive Strength in Uniaxial Fiber-Metal Matrix Composites,” Journal of AIAA, Vol. 4, 1966, 102-106.
134. Hashin, Z., “Transverse Strength” in Dow, N.F., and Rosen, B. W., “Evaluation of Filament Reinforced Composites for Aerospace Structural Applications,” NASA CR-207, 1965, pp. 36-43.
135. Shu, L., S., and Rosen, B. W., “Strength of Fiber Reinforced Composites by Limit Analysis Method,” Journal of Composite Materials, Vol. 1, 1967, pp. 366-381.
136. McLaughlin, P. V., “Limit Behavior of Fibrous Materials,” International Journal of Solids and Structures, Vol. 6, 1970, pp. 1357-1376.
137. McLaughlin, P. V., “Plastic Limit Behavior and Failure of Filament Reinforced Materials,” International Journal of Solids and Structures, Vol. 8, 1972, pp. 1299-1318.
138. Majumdar, S., and McLaughlin, P. V., “Upper Bounds to In-Plane Shear Strength of Unidirectional Fiber Composites,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 40, 1973, pp. 824-825.
139. Rosen, B. W., “Strength of Uniaxial Fibrous Composites,” in Mechanics of Composite Materials, Pergamon Press, 1970, pp. 621-651.
140. Chamis, C. C., “Micromechanics Strength Theories,” in Fracture and Fatigue, Vol. 5 of Composite Materials, Academic Press, New York, 1974, pp. 93-151.
141. Wu, E. M., “Phenomenological Anisotropic Failure Criterion,” in Mechanics of Composite Materials, Vol. 2 of Composite Materials, Academic Press, New York, 1974, pp. 353-431.
142. Tsai, S. W., “Strength Characteristics of Composite Materials,” NASA CR-224, 1965.
143. Hill, R., “A Theory of the Yielding and Plastic Flow of Anisotropic Materials,” Proceedings of the Royal Society, London, Series A, Vol. 193, 1948, pp. 281-290.
144. Hoffman, O., “The Brittle Strength of Orthotropic Materials,” Journal of Composite Materials, Vol. 1, 1967, pp. 200-206.
145. Tsai, S. W., and Wu, E. M., “A General Theory of Strength for Anisotropic Materials,” Journal of Composite Materials, Vol. 5, 1971, pp. 58-81.
146. Hashin, Z., “Failure Criteria for Unidirectional Fiber Composites,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 47, 1980, pp. 329-334.
147. Hashin, Z., and Rotem, A., “A Fatigue Failure Criterion for Fiber-Reinforced Materials,” Journal of Composite Materials, Vol. 7, 1973, pp. 448-464.
148. Pipes, R. B., and Cole, B. W., “On the Off-Axis Strength Test for Anisotropic Materials,” Journal of Composite Materials, Vol. 7, 1973, pp. 246-256.
149. Kim, R. Y., “On the Off-Axis and Angle-Ply Strength of Composites,” in Test Methods and Design Allowables for Fibrous Composites, ASTM, STP 734, 1981, pp. 281-337.
150. Hashin, Z., “Fatigue Failure Criteria for Undirectional Fiber Composites,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 48, 1981, pp. 846-852.
151. Awerbuch, J., and Hahn, H. T., “Off-Axis Fatigue of Graphite/Epoxy Composite,” in Fatigue of Fibrous Composite Materials, ASTM, STP 723, 1981, pp. 243-273.
152. Talreja, R., “Fatigue of Composite Materials: Damage Mechanisms and Fatigue-Life Diagrams,” Proceedings of the Royal Society, London, Series A, Vol. 378, 1981, pp. 461-475.
153. Halpin, J. C., Jerina, K. L., and Johnson, T. A., “Characterization of Composites for the Purpose of Reliability Evaluation,” in Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM, STP 521, 1973, pp. 5-64.
154. Yang, J. N., and Jones, D. L., “Load Sequence Effects on the Fatigue of Unnotched Composite Materials,” in Fatigue of Fibrous Composite Materials, ASTM, STP 723, 1981, pp. 213-231.
155. Broutman, L. J., and Sahu, S., “A New Theory to Predict Cumulative Fatigue Damage in Fiberglass Reinforced Plastics,” in Composite Materials: Testing and Design, ASTM, STP 497, 1972, pp. 170-188.
156. Hashin, Z., and Rotem, A., “A Cumulative Damage Theory of Fatigue Failure,” Materials Science and Engineering, Vol. 34, 1978, pp. 147-160.
157. Hashin, Z., “Statistical Cumulative Damage Theory for Fatigue Life Prediction,” ASME JOURNAL OF APPLIED MECHANICS, in press.
158. Reifsnider, K. L., “Some Fundamental Aspects of Damage in Composite Laminates,” Proceedings 14th Annual Meeting of Society of Engineering Science, Bethlehem, Pa., 1977, pp. 373-384.
159. Reifsnider, K. L., Henneke, E. G., Stinchcomb, N. W., and Duke, J. C., “Damage Mechanics and NDE of Composite Laminates,” in Mechanics of Composite Materials: Recent Advances, Proceedings IUTAM Symposium on Mechanics of Composite Materials, Hashin, Z., and Herakovich, C. T., eds., Pergamon Press, 1983.
160. Hahn, H. T., “Nonlinear Behavior of Laminated Composites,” Journal of Composite Materials, Vol. 7, 1973, pp. 257-271.
161. Hashin, Z., Bagchi, D., and Rosen, B. W., “Non-Linear Behavior of Fiber Composite Laminates,” NASA CR-2313, 1974.
162. Rotem, A., and Hashin, Z., “Fatigue Failure of Angle Ply Laminates,” AIAA Journal, Vol. 14, 1976, pp. 868-872.
163. Hahn, H. T., “Fatigue Behavior and Life Prediction of Composite Laminates,” in Composite Materials: Testing and Design, ASTM, STP 674, 1979, pp. 383-417.
164. O’Brien, T. K., and Reifsnider, K. L., “Fatigue Damage Evaluation Through Stiffness Measurements in Boron-Epoxy Laminates,” Journal of Composite Materials, Vol. 15, 1981, pp. 55-70.
165. Rotem, A., “Fatigue Failure Mechanism of Composite Laminates,” in Mechanics of Composite Materials: Recent Advances, Proceedings IUTAM Symposium on Mechanics of Composite Materials, Hashin, Z., and Herakovich, C. T., eds., Pergamon Press, 1983.
166. Pipes, R. B., and Pagano, N. J., “Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension,” Journal ofComposite Materials, Vol. 4, 1970, pp. 538-548.
167. Soni, S. R., and Pagano, N. J., “Elastic Response of Composite Laminates,” in Mechanics of Composite Materials: Recent Advances. Proceedings IUTAM Symposium on Mechanics of Composite Materials, Hashin, Z., and Herakovich, C. T., eds., Pergamon Press, 1983.
168. Wang, S. S., and Choi, I., “Boundary Layer Effects in Composite Laminates,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 49, 1982, “Part 1-Free-Edge Singularities,” pp. 541-548, “Part 2-Free-Edge Solutions and Basic Characteristics,” pp. 549-560.
169. Wang, S. S., and Choi, I., “Influence of Fiber Orientation and Ply Thickness on Hygroscopic Boundary-Layer Stresses in Angle-Ply Composite Laminates,” Journal of Composite Materials, Vol. 16, 1982, pp. 244-258.
170. Herakovich, C. T., Nagarkar, A., and O’Brien, D. A., “Failure Analysis of Composite Laminates With Free Edges,” in Modern Developments in Composite Materials and Structures, ASME, 1979, pp. 53-66.
171. Herakovich, C. T., “On the Relationship Between Engineering Properties and Delamination of Composite Materials,” Journal of Composite Materials, Vol. 15, 1981, pp. 336-348.
172. Rosen, B. W., “Failure of Fiber Composite Laminates,” in Mechanics of Composite Materials: Recent Advances, Proceedings IUTAM Symposium on Mechanics of Composite Materials, Hashin, Z., and Herakovich, C. T., eds., Pergamon Press, 1983.
173. Aboudi, J., “The Effective Moduli of Short-Fiber Composites,” International Journal of Solids and Structures, in press, 1983.
174. Kennett, B. L. N., “Elastic Wave Propagation in Stratified Media,” in Advances in Applied Mathematics, Vol. 21, Yih, C. S., ed., Academic Press, New York, 1981, pp. 80-167.
175. Min, B. K., “A Plane Stress Formulation for Elastic Plastic Deformation of Unidirectional Composites,” Journal of the Mechanics and Physics of Solids, Vol. 29, 1981, p. 327-352.
176. Aboudi, J., “Effective Behavior of Inelastic Fiber-Reinforced Composites,” International Journal of Engineering Sciences, in press.
177. Watt, P. J., “The Elastic Properties of Composite Materials,” Reviews of Geophysics and Space Physics, Vol. 14, 1976, pp. 541-563.