Dynamically Expanding Eshelby Inclusions and Inhomogeneity Boundaries

这笔赠款的研究目标是为动态加载下固体中的缺陷创建基本解决方案，这些缺陷涉及动态膨胀夹杂物，即材料内具有一般相变应变的区域(例如由于受基质约束的热膨胀)，以及关于扩展不均匀性的解决方案(材料特性随着相变应变区域的扩展而变化的区域)。这些解决方案将允许计算“驱动力”，即需要提供的机械作功速率，以动态地创建具有相变应变的夹杂/不均匀的增量区域，从而计算这些区域在动态加载下的演化。这一现象的静态对应物是“EShelby夹杂”和不均匀，它构成了过去50年来固体力学中被引用最多的论文。这些理论预测将用于对应力波作用下形状记忆合金相变微观结构演化实验结果的分析建模，这些动态解在表征材料微观结构的动态演化方面具有广泛的应用和影响，例如在生物医学设备中广泛使用的形状记忆合金的微观结构的动态演化，以及在震源的地球物理模拟中。这项研究工作将对加州大学圣地亚哥分校(UCSD)和全国范围内的材料动力学性质和微观结构演变的研究生教育计划产生影响。

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.