Analysis of Composite Materials—A Survey

The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure.

[1]  A. Einstein.  Eine neue Bestimmung der Moleküldimensionen , 1905 .

[2]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[3]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen , 1935 .

[4]  D. A. G. Bruggeman.  Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. II. Dielektrizitätskonstanten und Leitfähigkeiten von Vielkristallen der nichtregulären Systeme , 1936 .

[5]  J. Dewey.  The Elastic Constants of Materials Loaded with Non‐Rigid Fillers , 1947 .

[6]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  R. Hill.  The Elastic Behaviour of a Crystalline Aggregate , 1952 .

[8]  William Fuller Brown,et al.  Solid Mixture Permittivities , 1955 .

[9]  E. H. Kerner,et al.  The Electrical Conductivity of Composite Media , 1956 .

[10]  E. H. Kerner.  The Elastic and Thermo-elastic Properties of Composite Media , 1956 .

[11]  E. Kröner.  Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[12]  B. Paul.  PREDICTION OF ELASTIC CONSTANTS OF MULTI-PHASE MATERIALS , 1959 .

[13]  Charles W. Tobias,et al.  Resistance to Potential Flow through a Cubical Array of Spheres , 1959 .

[14]  J. R. Bristow.  Microcracks, and the static and dynamic elastic constants of annealed and heavily cold-worked metals , 1960 .

[15]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of polycrystals , 1962 .

[16]  S. Shtrikman,et al.  On some variational principles in anisotropic and nonhomogeneous elasticity , 1962 .

[17]  Zvi Hashin,et al.  The Elastic Moduli of Heterogeneous Materials , 1962 .

[18]  S. Shtrikman,et al.  A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials , 1962 .

[19]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[20]  M. Beran,et al.  Statistical properties of the electric field in a medium with small random variations in permittivity , 1963 .

[21]  Zvi Hashin,et al.  THEORY OF MECHANICAL BEHAVIOR OF HETEROGENEOUS MEDIA , 1963 .

[22]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[23]  Joseph B. Keller,et al.  A Theorem on the Conductivity of a Composite Medium , 1964 .

[24]  Z. Hashin,et al.  The Elastic Moduli of Fiber-Reinforced Materials , 1964 .

[25]  B. W. Rosen,et al.  Tensile failure of fibrous composites. , 1964 .

[26]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour , 1964 .

[27]  Zvi Hashin,et al.  Viscoelastic Behavior of Heterogeneous Media , 1965 .

[28]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[29]  R. Meister,et al.  Variational Method of Determining Effective Moduli of Polycrystals: (A) Hexagonal Symmetry, (B) Trigonal Symmetry , 1965 .

[30]  Zvi Hashin,et al.  On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry , 1965 .

[31]  J. B. Walsh.  The effect of cracks on the compressibility of rock , 1965 .

[32]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials—III. self-consistent model , 1965 .

[33]  Stephen W. Tsai,et al.  Strength Characteristics of Composite Materials. , 1965 .

[34]  Zvi Hashin.  Elasticity of Random Media , 1965 .

[35]  B. W. Rosen,et al.  Mechanics of composite strengthening. , 1965 .

[36]  J. B. Walsh.  The effect of cracks on the uniaxial elastic compression of rocks , 1965 .

[37]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[38]  N. F. Dow,et al.  Evaluations of Filament-Reinforced Composites for Aerospace Structural Applications. , 1965 .

[39]  L. Walpole.  On bounds for the overall elastic moduli of inhomogeneous systems—I , 1966 .

[40]  Zvi Hashin,et al.  Viscoelastic fiber reinforced materials. , 1966 .

[41]  Tai Te Wu,et al.  The effect of inclusion shape on the elastic moduli of a two-phase material* , 1966 .

[42]  ANALYTICAL PROCEDURES FOR PREDICTING THE MECHANICAL PROPERTIES OF FIBER REINFORCED COMPOSITES. PART III. , 1966 .

[43]  D. Adams,et al.  MECHANICAL BEHAVIOR OF FIBER-REINFORCED COMPOSITE MATERIALS. , 1967 .

[44]  C.H. Chen,et al.  Mechanical Properties of Fiber Reinforced Composites , 1967 .

[45]  O. Hoffman.  The Brittle Strength of Orthotropic Materials , 1967 .

[46]  John M. Hedgepeth,et al.  Local Stress Concentrations in Imperfect Filamentary Composite Materials , 1967 .

[47]  B. W. Rosen,et al.  Strength of Fiber-Reinforced Composites by Limit Analysis Methods , 1967 .

[48]  George S. Springer,et al.  Thermal Conductivities of Unidirectional Materials , 1967 .

[49]  Richard Schapery.  Thermal Expansion Coefficients of Composite Materials Based on Energy Principles , 1968 .

[50]  Zvi Hashin,et al.  Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites , 1968 .

[51]  R. Christensen,et al.  Viscoelastic properties of heterogeneous media , 1969 .

[52]  Bounds for the real and imaginary parts of the dynamic moduli of composite viscoelastic systems , 1969 .

[53]  S. Prager,et al.  Improved Variational Bounds on Some Bulk Properties of a Two‐Phase Random Medium , 1969 .

[54]  J. Achenbach,et al.  WAVE PROPAGATION IN LAMINATED AND FIBER-REINFORCED COMPOSITES , 1970 .

[55]  Steven C. Batterman,et al.  Limit behavior of fibrous materials , 1970 .

[56]  B. W. Rosen,et al.  A statistical theory of material strength with application to composite materials , 1970 .

[57]  Zvi Hashin,et al.  Effective thermal expansion coefficients and specific heats of composite materials , 1970 .

[58]  N. J. Pagano,et al.  Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension , 1970 .

[59]  Zvi Hashin,et al.  THEORY OF COMPOSITE MATERIALS , 1970 .

[60]  B. Rosen.  STRENGTH OF UNIAXIAL FIBROUS COMPOSITES , 1970 .

[61]  M. Beran,et al.  Mean field variations in a statistical sample of heterogeneous linearly elastic solids , 1970 .

[62]  Zvi Hashin,et al.  Complex moduli of viscoelastic composites—I. General theory and application to particulate composites , 1970 .

[63]  V. Levin.  The relation between mathematical expectations of stress and strain tensors in elastic microheterogeneous media , 1971 .

[64]  Effective Electrical, Thermal and Magnetic Properties of Fiber Reinforced Materials , 1971 .

[65]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[66]  Zvi Hashin,et al.  Theory of fiber reinforced materials , 1972 .

[67]  G. Batchelor,et al.  The determination of the bulk stress in a suspension of spherical particles to order c2 , 1972, Journal of Fluid Mechanics.

[68]  B. W. Rosen,et al.  Tensile failure criteria for fiber composite materials , 1972 .

[69]  P. V. McLaughlin,et al.  Plastic limit behavior and failure of filament reinforced materials , 1972 .

[70]  R. Roscoe.  Improved bounds for real and imaginary parts of complex moduli of isotropic viscoelastic composites , 1972 .

[71]  Lj Broutman,et al.  A New Theory to Predict Cumulative Fatigue Damage in Fiberglass Reinforced Plastics , 1972 .

[72]  R. Pipes,et al.  On the Off-Axis Strength Test for Anisotropic Materials1 , 1973 .

[73]  John C. Halpin,et al.  Characterization of Composites for the Purpose of Reliability Evaluation , 1973 .

[74]  D. Jeffrey,et al.  Conduction through a random suspension of spheres , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[75]  J. Korringa.  Theory of elastic constants of heterogeneous media , 1973 .

[76]  H. T. Hahn,et al.  Nonlinear Behavior of Laminated Composites , 1973 .

[77]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[78]  D. D. Yue,et al.  Theory of Electric Polarization , 1974 .

[79]  Z. Hashin,et al.  Non-linear behavior of fiber composite laminates , 1974 .

[80]  Jack C. Smith.  Correction and Extension of van der Poel's Method for Calculating the Shear Modulus of a Particulate Composite. , 1974, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[81]  S. Boucher.  On the Effective Moduli of Isotropic Two-Phase Elastic Composites , 1974 .

[82]  Fumiko Yonezawa,et al.  Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. V. One− and two−dimensional systems , 1975 .

[83]  George Herrmann,et al.  WEAKENING OF AN ELASTIC SOLID BY A RECTANGULAR ARRAY OF CRACKS , 1975 .

[84]  M. Beran,et al.  On the effective thermal conductivity of a random suspension of spheres , 1976 .

[85]  Z. Hashin,et al.  Fatigue failure of angle ply laminates , 1976 .

[86]  On the conductivity of fiber reinforced materials , 1976 .

[87]  B. Budiansky,et al.  Elastic moduli of a cracked solid , 1976 .

[88]  Z. Hashin,et al.  Bounds for effective permittivities of lossy dielectric composites , 1976 .

[89]  E. Kröner.  Bounds for effective elastic moduli of disordered materials , 1977 .

[90]  Concerning the effective transverse conductivity of a two-dimensional two-phase material , 1977 .

[91]  R. Mclaughlin.  A study of the differential scheme for composite materials , 1977 .

[92]  M. Hori.  Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. VII. Comparison of different approaches , 1977 .

[93]  Z. Hashin,et al.  A CUMULATIVE DAMAGE THEORY OF FATIGUE FAILURE , 1978 .

[94]  N. Laws,et al.  Self-consistent estimates for the viscoelastic creep compliances of composite materials , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[95]  David J. Bergman,et al.  The dielectric constant of a composite material—A problem in classical physics , 1978 .

[96]  D. R. McKenzie,et al.  The conductivity of lattices of spheres I. The simple cubic lattice , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[97]  S. L. Phoenix,et al.  The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials I: Analysis and Conjectures , 1978 .

[98]  C. T. Herakovich,et al.  Failure analysis of composite laminates with free edges , 1979 .

[99]  J. Watt,et al.  Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry , 1979 .

[100]  Z. Hashin.  Analysis of Properties of Fiber Composites With Anisotropic Constituents , 1979 .

[101]  S. Phoenix,et al.  Statistical Aspects of Failure of Fibrous Materials , 1979 .

[102]  R. Christensen,et al.  Solutions for effective shear properties in three phase sphere and cylinder models , 1979 .

[103]  Alan Hoenig,et al.  Elastic moduli of a non-randomly cracked body , 1979 .

[104]  H. T. Hahn,et al.  Fatigue Behavior and Life Prediction of Composite Laminates , 1979 .

[105]  Z. Hashin.  Failure Criteria for Unidirectional Fiber Composites , 1980 .

[106]  R. Pipes.  Boundary layer effects in composite laminates , 1980 .

[107]  J. Willis,et al.  A polarization approach to the scattering of elastic waves—II. Multiple scattering from inclusions , 1980 .

[108]  Z. Hashin,et al.  EFFECTIVE ELASTIC MODULI OF CRACKED FIBER COMPOSITES , 1980 .

[109]  J. Watt,et al.  Clarification of the Hashin‐Shtrikman bounds on the effective elastic moduli of polycrystals with hexagonal, trigonal, and tetragonal symmetries , 1980 .

[110]  Tsu-Wei Chou,et al.  A Self-Consistent Approach to the Elastic Stiffness of Short-Fiber Composites , 1980 .

[111]  Graeme W. Milton,et al.  Bounds on the complex dielectric constant of a composite material , 1980 .

[112]  David J. Bergman,et al.  Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material , 1980 .

[113]  J. Watt,et al.  An experimental investigation of the Hashin-Shtrikman bounds on two-phase aggregate elastic properties , 1980 .

[114]  B. Kennett.  Elastic Wave Propagation in Stratified Media , 1981 .

[115]  Jonathan Awerbuch,et al.  Off-Axis Fatigue of Graphite/Epoxy Composite , 1981 .

[116]  B. Min.  A plane stress formulation for elastic-plastic deformation of unidirectional composites , 1981 .

[117]  J. N. Yang,et al.  Load sequence effects on the fatigue of unnotched composite materials , 1981 .

[118]  K. Reifsnider,et al.  Fatigue Damage Evaluation through Stiffness Measurements in Boron-Epoxy Laminates , 1981 .

[119]  Zvi Hashin,et al.  Fatigue Failure Criteria for Unidirectional Fiber Composites , 1981 .

[120]  R. Talreja,et al.  Fatigue of composite materials: damage mechanisms and fatigue-life diagrams , 1981, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[121]  J. Willis,et al.  Variational and Related Methods for the Overall Properties of Composites , 1981 .

[122]  L. Walpole.  Elastic Behavior of Composite Materials: Theoretical Foundations , 1981 .

[123]  J. McCoy.  Macroscopic Response of Continua with Random Microstructures , 1981 .

[124]  Carl T. Herakovich,et al.  On the Relationship between Engineering Properties and Delamination of Composite Materials , 1981 .

[125]  On the Off-Axis and Angle-Ply Strength of Composites , 1981 .

[126]  Su Su Wang,et al.  Influence of Fiber Orientation and Ply Thickness on Hygroscopic Boundary-Layer Stresses in Angle-Ply Composite Laminates , 1982 .

[127]  Graeme W. Milton,et al.  Bounds on the elastic and transport properties of two-component composites , 1982 .

[128]  A. Rotem.  FATIGUE FAILURE MECHANISM OF COMPOSITE LAMINATES , 1983 .

[129]  J. Duke,et al.  DAMAGE MECHANICS AND NDE OF COMPOSITE LAMINATES , 1983 .

[130]  Zvi Hashin,et al.  Statistical Cumulative Damage Theory for Fatigue Life Prediction , 1983 .

[131]  Jacob Aboudi,et al.  The effective moduli of short-fiber composites , 1983 .

[132]  B. Rosen.  FAILURE OF FIBER COMPOSITE LAMINATES , 1983 .

[133]  Jacob Aboudi,et al.  Effective behavior of inelastic fiber-reinforced composites , 1984 .

[134]  Z. Hashin,et al.  Mechanics of Composite Materials: Recent Advances , 1984 .