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

所提出的工作考虑了线弹性断裂 有限塑性下的动态载荷下的材料 方面的影响. 采用微观力学观点， 由晶体缺陷或位错的阵列表示。 这些 在一系列理想化的瞬态问题中进行研究。 这 短暂的性质本身就将工作与许多现有的工作区分开来。 裂纹位错研究 这样的分析必须面对数学上的困难， 出现在准静态研究中。 然而，长度尺度和波 传播方面的考虑， 分析，解决方案。 拟议工作的一项主要任务是 边界/初始值问题解决方案开发。

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.