Micromechanics of Composite Materials

Abstract

1 Tensor component and matrix notation.- 2 Anisotropic elastic solids.- 2.1 Elastic strain energy density.- 2.2 Material symmetries.- 2.3 Transversely isotropic composite materials.- 2.4 Cylindrically orthotropic materials.- 2.5 Young's modulus, shear modulus and Poisson's ratio.- 3 Elementary concepts and tools.- 3.1 Aggregates and constituent phases.- 3.2 Herogeneous microstructures.- 3.3 Representative volume.- 3.4 Local and overall stress and strain fields.- 3.5 Overall properties and local fields.- 3.6 Transformation fields.- 3.7 Work, energy and reciprocal theorems.- 3.8 The Levin formula and the Hill lemma.- 3.9 Universal connections for elastic moduli of fibrous composites.- 3.10 Constitutive relations and local fields in heterogeneous aggregates.- 4 Inclusions, inhomogeneities and cavities.- 4.1 Homogeneous ellipsoidal inclusions: The Eshelby solution.- 4.2 Ellipsoidal inhomogeneities: The equivalent inclusion method.- 4.3 Transformed inhomogeneities.- 4.4 Dilute approximation of overall properties.- 4.5 Green's function and Eshelby's tensor in elastic solids.- 4.6 Coefficients of the P tensors for selected ellipsoidal shapes.- 4.7 Summary of principal results.- 5 Energies of inhomogeneities, dilute reinforcements and cracks.- 5.1 Energy changes caused by mechanical loads.- 5.2 Energy changes caused by uniform phase eigenstrains.- 5.3 Energy changes caused by mechanical loads and phase eigenstrains.- 5.4 Energy and stiffness changes caused by cracks.- 6 Evaluations and bounds on elastic moduli of heterogeneous materials.- 6.1 Elementary energy bounds.- 6.2 Hashin-Shtrikman and Walpole bounds on overall elastic moduli.- 6.3 Evaluation of H-S bounds for ellipsoidal inhomogeneities.- 6.4. Composite element assemblage bounds.- 6.5 The generalized self-consistent method.- 7 Estimates of mechanical properties of composite materials.- 7.1 The self-consistent method (SCM).- 7.2 The Mori-Tanaka method (M-T).- 7.3 The differential scheme.- 7.4 The double inclusion and double inhomogeneity models.- 7.5 Applications of SCM and M-T to functionally graded materials.- 8 Transformation fields.- 8.1 Uniform change of temperature in two-phase composites and polycrystals.- 8.2 Transformation influence functions and concentration factors.- 8.3 Uniform change in temperature in multiphase systems.- 8.4 Capabilities of bounds and estimates of overall and local fields.- 9 Interfaces and interphases.- 9.1 Perfectly bonded interfaces.- 9.2 Imperfectly bonded inhomogeneities and cavities.- 10 Symmetric laminates.- 10.1 Constitutive relations of fibrous plies.- 10.2 Coordinate systems and transformations.- 10.3 Overall response and ply stresses in symmetric laminates.- 10.4 Ply and constituent stress and strain averages .- 10.5 Design of laminates for cylindrical pressure vessels.- 10.6 Dimensionally stable laminates.- 10.7 Auxetic laminates.- 10.8 Laminates with reduced free edge stresses.- 11 Elastic-plastic solids.- 11.1 Yield and loading surfaces, normality and convex.- 11.2 Hardening and flow rules.- 11.3 Matrix form and consistency of the instantaneous tangent stiffness.- 12 Inelastic composite materials.- 12.1 Transformation field analysis (TFA) of inelastic deformation.- 12.2 Experimental support of theoretical predictions.- 12.3 Thermal hardening.- References.