Modeling and Analysis of the Mechanical Behavior of Advanced Engineering Materials at the Micro- and Nano-scales

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A crucial part of the process of designing, developing or testing of advanced materials and composite material structures is concerned with the prediction of the behavior of the material or structure when subjected to various loading configurations and environmental conditions. One extremely effective method of doing this in terms of both cost and time is to 'build' a mathematical model. The latter can then be used repeatedly to analyze the response of the material or structure to various different operational circumstances. The information obtained then allows engineers to design and develop the most effective and cost-efficient assembly for a specified purpose. The key to designing an effective mathematical model is to understand the salient features of the behavior of the material or structure and ensure that these are captured correctly in the model. This, however, must be balanced against the requirement that the model is not overly complicated and is convenient to use. In this research, the applicant will continue to apply his expertise in continuum mechanics and analytical techniques to devise new and extend existing mathematical models describing the behavior of advanced materials and material structures at the nano- and micro-scales. In particular, recognizing the key contribution of material surfaces at the nano-scale, the applicant will continue his work in the development of efficient, well-posed and numerically-stable models which incorporate the most effective description of these 'surface effects' in nano-mechanics. These models have been shown also to be applicable at the micro-scale providing a more accurate prediction of material behavior which has led to the elimination of many of the contradictions and inadequacies of existing mathematical models. In addition, at the micro-scale, we continue our research into the analysis of models of composite materials where the design involves the introduction of material inhomogeneities (e.g. in the design of fibre-reinforced composites) as well as in the prediction of the behavior of advanced materials for which experiments show that microstructure plays a significant role (such materials include bone and ligament as well as synthetic composites, cellular solids and tortuous rock).