Micromechanics of Composite Materials (eBook)

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.