Modelling and Analysis of Advanced Composite Materials with Significant Microstructure

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In recent years fiber reinforced polymer composites (FRPs) and functionally graded materials (FGMs) have revolutionized aerospace, automotive, biomedical, building and bridge construction and sports equipment fields. This can be attributed to the fact that these materials have exceptional mechanical and chemical properties, including light weight, high specific strength, and fatigue and corrosion resistance. Such characteristics lead to important energy and material savings, improvements in the reliability of automobiles, residential structures, pipes, dental implants and therefore contribute to the economic benefits for all Canadians. Today the production and use of FRPs and FGMs constitute a multi-billion dollar industry.However, there exist formidable difficulties in understanding the elastic behavior of FRPs and FGMs which may have a negative effect on the quality of manufacturing and on the prediction of the material behaviour under complex types of loading.Many experimental studies have been performed lately to explain the elastic behaviour of FRPs and FGMs. However, not many attempts have been made to explain the experimental results from the theoretical viewpoint. Theoretical predictions of the elastic behavior of FRPs and FGMs are difficult because these materials possess a microstructure which has a significant effect on the overall properties of the materials. The presence of the microstructure makes it difficult to model the processes occurring in these materials using classical solid mechanics.The objective of this research is to develop a comprehensive model, which would allow us to predict the material behaviour of FRPs and FGMs in the cases when microstructure is significant and to obtain a reliable theoretical basis which can be used in practical design projects to avoid critical mistakes in the process of manufacturing of these materials. To achieve this objective we will be using the latest accomplishments of the theory of Micropolar Elasticity, which has been developed to describe deformations of materials when the microstructure is significant. The physical nature of these materials requires the asymmetric description of deformation which leads to more complicated models than those considered in classical solid mechanics.In the past ten years the applicant has achieved significant progress in modelling the behaviour of materials with significant microstructure. This research is another step towards the goal of developing a universal generalized approach within the foundations of continuum mechanics for the description of the elastic behavior of new advanced materials. The program will employ 4 PhD and 4 M.Sc. students within the next five years. They will study the latest developments of solid mechanics and advanced mathematical modelling and will develop into the leading scientists in the emerging area of high economic importance in Canada.