Dvorak G. Micromechanics of Composite Materials

Springer Science+Business Media B.V., 2013, XVII, 442 p. 68 illus. — ISBN: 978-94-007-4100-3, ISBN: 978-94-007-4101-0 (eBook), DOI 10.1007/978-94-007-4101-0 — (Solid Mechanics and its Applications Volume 186).Basic theory presented in simple matrix notation
Contains many new subjects that have not yet appeared in book form
Chapter summaries outlining equation sequences to be used in accomplishing selected tasks
This book presents a broad exposition of analytical and numerical methods for modeling composite materials, laminates, polycrystals and other heterogeneous solids, with emphasis on connections between material properties and responses on several length scales, ranging from the nano and microscales to the macroscale.Many new results and methods developed by the author are incorporated into a rich fabric of the subject, which has been explored by several researchers over the last 40 years. The first part of the book reviews anisotropic elasticity theory, and then it describes the frequently used procedures and theorems for bounding and estimating overall properties, local fields and energy changes in elastic inhomogeneities, heterogeneous media, fiber composites and functionally graded materials. Those are caused by mechanical loads and by phase eigenstrains, such as thermal, transformation and inelastic strains, and also by cavities and cracks. Worked examples show that the eigendeformations may contribute a major part of the overall response and of interior stress and strain fields in the constituents. Separate attention is given to perfect and imperfect interfaces, and to evaluation of interface stresses induced by mechanical and transformation loads. Micromechanical methods are extended to analysis of symmetric laminates. Applications include design of laminate configurations for pressure vessels, for dimensionally stable and auxetic laminates, for laminates with reduced free edge stresses and with fiber prestress, and for those sustaining damage by transverse cracking and fiber breaks. A review of the incremental theory of plasticity, of the transformation field analysis method, and of modeling and experimental results for metal matrix composites, are extensively described in the closing chapters.
This volume is intended for advanced undergraduate and graduate students, researchers and engineers interested and involved in analysis and design of composite structures.Content Level » Research
Keywords » composite materials - heterogeneous solids - metal matrix composites - solid mechanics - transformation strains
Related subjects » Classical Continuum Physics - Mechanics - Special types of MaterialsTensor component and matrix notationAnisotropic elastic solidsElastic strain energy density
Material symmetries
Transversely isotropic composite materials
Cylindrically orthotropic materials
Young’s modulus, shear modulus and Poisson’s ratioElementary concepts and toolsAggregates and constituent phases
Herogeneous microstructures
Representative volume
Local and overall stress and strain fields
Overall properties and local fields
Transformation fields
Work, energy and reciprocal theorems
The Levin formula and the Hill lemma
Universal connections for elastic moduli of fibrous composites
Constitutive relations and local fields in heterogeneous aggregatesInclusions, inhomogeneities and cavitiesHomogeneous ellipsoidal inclusions: The Eshelby solution
Ellipsoidal inhomogeneities: The equivalent inclusion method
Transformed inhomogeneities
Dilute approximation of overall properties
Green's function and Eshelby's tensor in elastic solids
Coefficients of the P tensors for selected ellipsoidal shapes
Summary of principal resultsEnergies of inhomogeneities, dilute reinforcements and cracksEnergy changes caused by mechanical loads
Energy changes caused by uniform phase eigenstrains
Energy changes caused by mechanical loads and phase eigenstrains
Energy and stiffness changes caused by cracksEvaluations and bounds on elastic moduli of heterogeneous materialsElementary energy bounds
Hashin-Shtrikman and Walpole bounds on overall elastic moduli
Evaluation of H-S bounds for ellipsoidal inhomogeneities
Composite element assemblage bounds
The generalized self-consistent methodEstimates of mechanical properties of composite materialsThe self-consistent method (SCM)
The Mori-Tanaka method (M-T)
The differential scheme
The double inclusion and double inhomogeneity models
Applications of SCM and M-T to functionally graded materialsTransformation fieldsUniform change of temperature in two-phase composites and polycrystals
Transformation influence functions and concentration factors
Uniform change in temperature in multiphase systems
Capabilities of bounds and estimates of overall and local fieldsInterfaces and interphasesPerfectly bonded interfaces
Imperfectly bonded inhomogeneities and cavitiesSymmetric laminatesConstitutive relations of fibrous plies
Coordinate systems and transformations
Overall response and ply stresses in symmetric laminates
Ply and constituent stress and strain averages
Design of laminates for cylindrical pressure vessels
Dimensionally stable laminates
Auxetic laminates
Laminates with reduced free edge stressesElastic-plastic solidsYield and loading surfaces, normality and convex
Hardening and flow rules
Matrix form and consistency of the instantaneous tangent stiffnessInelastic composite materialsTransformation field analysis (TFA) of inelastic deformation
Experimental support of theoretical predictions
Thermal hardening.- References