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

先进材料和复合材料结构的设计、开发或测试过程的一个关键部分是预测材料或结构在各种载荷配置和环境条件下的行为。在成本和时间方面，一个非常有效的方法是“建立”一个数学模型。然后，后者可以反复用于分析材料或结构对各种不同操作环境的响应。然后，获得的信息使工程师能够设计和开发用于特定目的的最有效和最具成本效益的组件。设计有效的数学模型的关键是理解材料或结构行为的显著特征，并确保这些特征在模型中被正确捕获。然而，这必须与模型不过于复杂和便于使用的要求相平衡。在这项研究中，申请人将继续运用他在连续介质力学和分析技术方面的专业知识，设计新的和扩展现有的数学模型，描述先进材料和材料结构在纳米和微米尺度上的行为。特别是，认识到材料表面在纳米尺度上的关键贡献，申请人将继续他的工作，在开发有效的，适定性和数值稳定的模型，其中包括最有效的描述，这些'表面效应'在纳米力学。这些模型也被证明适用于微观尺度，提供了更准确的材料行为预测，从而消除了现有数学模型的许多矛盾和不足之处。此外，在微观尺度上，我们继续研究复合材料模型的分析，其中设计涉及材料不均匀性的引入（例如，在纤维增强复合材料的设计中）以及在先进材料的行为预测中，实验表明微观结构起着重要作用（这些材料包括骨头和韧带以及合成复合材料、多孔固体和弯曲的岩石）。

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).