Mathematical Sciences: Transient Studies of Dislocation-based Micromechanical Effects in Fracture

提出的工作考虑了线弹性材料在有限塑性作用下的动载断裂。采用微观力学的观点，用晶体缺陷或位错阵列来表示其影响。这些都是在一系列理想化的瞬态问题中进行研究的。这种瞬态性质本身将这项工作与许多现有的裂纹-位错研究区分开来。这种分析必须面对准静态研究中不会出现的数学困难。然而，长度尺度和波传播的考虑对精确的、最好是解析的解决方案给予了重视。建议的工作的主要任务是在边界/初始值问题的解决方案的发展。

The work proposed considers the fracture of linearly elastic materials under dynamic loading in the presence of limited plastic effects. A micromechanical view is adopted, and the effects represented by arrays of crystals defects, or dislocations. These are studied in a series of idealized, transient problems. This transient nature itself distinguishes the work from many existing crack-dislocation studies. Such analyses must confront mathematical difficulties which do not arise in quasi-static studies. Nevertheless, length scale and wave propagation considerations place a premium on exact, preferably analytic, solutions. A major task of the proposed work is in boundary/initial value problem solution development.