Dynamically Expanding Eshelby Inclusions and Inhomogeneity Boundaries

该基金的研究目标是为动态载荷下固体中涉及动态扩展夹杂物的缺陷创建基本解决方案，动态扩展夹杂物是材料内部具有一般转变应变的区域（例如由于受基体约束的热膨胀），以及关于扩展不均匀性的解决方案（材料性能随着转变应变区域的扩展而变化的区域）。该解决方案将允许计算“驱动力”，即需要提供的机械功速率，以动态地创建包含/不均匀性的增量区域和转换应变，因此，这些区域在动态加载下的演变。这种现象的静态对应部分是“Eshelby包容”和非均匀性，这是近50年来固体力学中被引用最多的论文。理论预测将用于形状记忆合金在应力波载荷作用下相变微观组织演变的实验结果的分析建模。这些动态解决方案的应用和影响在材料微观结构动态演变的表征方面是广泛的，例如在生物医学设备中广泛使用的形状记忆合金之一，以及在震源的地球物理建模中。这项研究成果将对加州大学圣地亚哥分校和全国范围内的材料动态特性和微观结构演变研究生教育项目产生影响。

The research objective of this grant is to create fundamental solutions for defects in solids under dynamic loading that concern dynamically expanding inclusions, which are regions within the material that possess general transformation strain (such as due to thermal expansion that is constrained by the matrix), and also solutions concerning expanding inhomogeneities (regions where the material properties change as the region of transformation strain expands). The solutions will allow the calculation of the "driving force," i.e. the mechanical rate of work needed to be supplied to create dynamically an incremental region of inclusion / inhomogeneity with transformation strain, and, consequently, the evolution of these regions under dynamic loading. The static counter-part of the phenomenon is the "Eshelby inclusion" and inhomogeneity, which constitutes the most cited paper in Solid Mechanics in the last fifty years. The theoretical predictions will be used in the analytical modeling of experimental results regarding the microstructural evolution of phase transformations in shape memory alloys due to stress wave loading.The applications and impact of these dynamic solutions are wide in the characterization of materials in terms of the dynamic evolution of their microstructure, such as the one of shape memory alloys widely used in biomedical devices, as well as in the geophysical modeling of earthquake sources. The research effort will have an impact on the graduate education program in the dynamical properties and microstructural evolution of materials at UCSD (University of California - San Diego) and nationwide.