Studies in Continuum Mechanics and Materials Science

这项研究旨在发展物质行为的现象学水平的数学模型。目标是为材料研究建立一个连续统一体的力学框架，为一般理论提供基础，并导致相关问题。提出了涉及非相干相变、原子扩散中的位错和晶界运动的研究。非线性连续介质力学和分析的日益联合促进了对材料的理解；重要的结果是理解缺陷和微观结构的新方法，以及在微观水平上预测宏观性质和详细行为的能力。这个项目旨在继续推进这一进程。

ABSTRACTThis research is toward developing mathematical models for materialbehavior at a phenomenological level. The goal is a continuum-mechanicalframework for the study of materials that provides a basis for generaltheories and leads to relevant problems. Proposed are studies involvingincoherent phase transitions, dislocations in the presence of atomicdiffusion, and grain-boundary motion.The growing alliance of nonlinear continuum mechanics and analysis hasled to significant advances in the understanding of materials; importantconsequences are new ways of understanding defects and microstructuresand the ability to predict macroscopic properties as well as detailedbehavior at the microscopic level. This project is meant to continuethis thrust.