On homogenization and de-homogenization of composite materials.

摘要

Composite homogenization is a modelling concept that allows the description of heterogeneous materials by constitutively equivalent, homogeneous ones. The concept is universally applied to fibrous composites, resulting in many modelling approaches. But, by homogenization, the composite is voided of its physical microstructure; elements that may affect failure mechanisms physically are also voided. This fact often leads to difficulties in failure theories formulated at the homogenized material scale.; De-homogenization is a reverse scheme in that the microstructure is restored, albeit locally, back in the homogenized composite. Clearly, this is done after composite homogenization and field analysis of composite structures under global loading; so the micro fields in the desired locations with restored microstructure can be recovered. The recovered micro fields may then provide the needed information for some failure theories to be formulated at the composite micro scale instead.; This thesis presents a unified modelling approach for homogenization (forward) and de-homogenization (backward), applicable to unidirectional composite systems. Emphasis is placed on the uniqueness between the forward and the backward modelling processes; so the desired micro fields are truly recovered within the confines of mechanics.; Micro fields in several laminates made of the UD systems are recovered; key effects that influence failure mechanisms therein are studied. An inter-scale failure theory that describes matrix cracking in laminates is then formulated, being based on the recovered micro-fields.; Laminate matrix cracking in several well-documented experimental studies are simulated using the inter-scale theory. The simulation captures the major cracking characteristics that are otherwise excluded in failure theories derived at the homogenized composite scale.; The general concept of homogenization/de-homogenization is applicable to all composite systems, where responses from micro-macro-global interactions are to be physically described. The approach taken in the formulation of the inter-scale theory serves as an example of both conceptual and practical importance.