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 theclosing chapters.

This volume is intended for advanced undergraduate and graduate students, researchers and engineers interested and involved in analysis and design of composite structures.

Inhalt
From the Content: History and overview.- Elastic constitutive relations.- Tensor component and matrix notations.- Decomposition of elastic constitutive relations.- Anisotropic elastic solids.- Elastic strain energy density.- Material symmetries.- Elements of material symmetry.- Triclinic materials.- Monoclinic materials.- Orthotropic material.-Trigonal and tetragonal materials.- Transversely isotropic or hexagonal materials.- Cubic materials.- Isotropic materials.- Transversely isotropic composite materials.- Engineering and Hill's moduli.- Walpole's notation.- Cylindrically orthotropic materials.- Young's modulus.