Mathematical Sciences: Studies in Continuum Mechanics and Materials Sciences

小行星9531221 该项目是一项研究工作的延续， 分析和统一表征材料的数学模型， 现象学层面的行为。该项目的长期目标是 一个研究材料的连续力学框架， 一般理论的基础，并导致边界值问题， 物理相关性。计划进行以下具体研究： 非相干相变的小应变理论的发展， 导致自由边界问题易于分析和计算; (ii)变形相变理论的发展 适合于完全刻面晶体;（iii）分析模型， 用曲率来概括运动。 这个项目的目标是一个连续力学框架的研究 的材料。 这一框架应成为制定 导致理解缺陷的新方法的一般理论， 微观结构，并提供预测宏观性能的能力， 以及微观层面的详细行为。

9531221 Gurtin This project is a continuation of a research effort toward developing, analyzing, and unifying mathematical models that characterize material behavior at a phenomenological level. The long-term goal of this project is a continuum-mechanical framework for the study of materials that provides a basis for general theories and leads to boundary-value problems of physical relevance. The following specific studies are planned: (i) the development of a small-strain theory of incoherent phase transitions that results in free-boundary problems amenable to analysis and computation; (ii) the development of a theory of deformational phase transitions appropriate to fully faceted crystals; (iii) the analysis of models that generalize motion by curvature. The goal of this project is a continuum mechanical framework for the study of materials. This framework should provide a basis for the development of general theories that lead to new ways of understanding defects and microstructures and provide an ability to predict macroscopic properties as well as detailed behavior at the microscopic level.