Elastic and inelastic micromechanical analysis of functionally graded materials and laminated structures using transformation fields

Micromechanical analysis of composites generally considers a representative volume of the composite subjected to boundary conditions derived from constant stress or strain fields. Certain microstructures can not be accurately analyzed by such methods. These include cases of composite plate bending, and functionally graded composites in which severe gradients in local reinforcement volume fraction may affect the effective properties.;In this thesis, the problem of a representative volume element (RVE) of the composite medium subjected to boundary conditions derived from linearly varying stress or strain fields is considered. Constraints on the form of the applied field are identified which produce simple solutions throughout the RVE. Constitutive relations are derived which relate stress and strain averages as well as stress and strain gradients in the RVE. Existing micromechanical techniques, including the Mori-Tanaka method (Mori and Tanaka, Acta. Met., 21, (1973)), are extended to generate estimates of these new stiffness matrices. This extended Mori-Tanaka formulation is used to estimate effective stiffness and thermal expansion of statistically homogeneous composites. The results reduce to the standard Mori-Tanaka solutions under appropriate conditions. Deviations from standard Mori-Tanaka estimates exist for certain microstructures and are in agreement with experimental results. Further generalizations are incorporated in order to consider severe reinforcement volume fraction gradients. Results indicate differences of as much as 25% in the effective properties for extreme cases when reinforcement volume fraction gradient effects are considered.;While the above results are useful in the elastic analysis of composites, transformation field analysis methods have certain advantages over other techniques in the inelastic analysis of composites (Dvorak, Proc. R. Soc. Lond. A, 437 (1992)). In this thesis, the fundamental concepts of transformation field analysis are extended to the case of boundary conditions derived from linearly varying stress or strain for cases in which the boundary conditions and applied transformation fields satisfy certain equilibrium constraints. A simplified form of the generalized relations is used within the assumptions of classical laminated plate theory to obtain closed form estimates of all required concentration factors. Further refinement of the method has the potential for efficient accurate plate analysis algorithms.