The expanding spherical inhomogeneity with transformation strain
The expanding spherical inhomogeneity with transformation strain
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DOI：
10.1007/s10704-011-9673-z
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发表时间：
2012-01
影响因子：
2.5
通讯作者：
X. Markenscoff
中科院分区：
文献类型：
--
作者：
X. Markenscoff
在线性弹性动力学的背景下，利用膨胀均匀球形夹杂的应变场(作为特征应变的函数)确定等效本征应变，在EShelby等效夹杂法的基础上，求出了具有膨胀变形应变(或本征应变)的非均匀(或不同弹性常数)球状夹杂在外加载荷作用下作一般运动扩张时的辐射场(包括惯量)。利用等效动态本征应变(依赖于边界运动)，可以得到非均匀球形膨胀夹杂的辐射场。在它们的基础上，可以计算出移动边界上的“驱动力”(自力)，这是创建具有本征应变的不均匀增量区域所需的机械功的速率(具有惯性)，即弹性常数随着本征应变区域的扩展而变化。自力依赖于运动的历史，在外加载荷存在的情况下，驱动力产生Peach-Koehler型力，该力表现出外加载荷与边界速度运动历史的耦合。
Within the context of linear elastodynamics, the radiated fields (including inertia) for a sphericalinhomogeneous(of different elastic constants) inclusion with dilatational transformation strain (or eigenstrain), expanding in general motion under applied loading, can been obtained on the basis of Eshelby’s equivalent inclusion method by using the strain field of the expandinghomogeneousspherical inclusion (as a function of the eigenstrain) to determine the equivalent eigenstrain. With the equivalent dynamic eigenstrain (which is dependent on the boundary motion), the radiated fields for the inhomogeneous spherical expanding inclusion can be obtained. Based on them, the “driving force” (self-force) on the moving boundary can be computed, and this is the rate of mechanical work (with inertia) required to create an incremental region of inhomogeneity with eigenstrain, i.e with the elastic constants changing as the region of the eigenstrain expands. The self-force depends on the history of the motion, and, in the presence of external loading the driving force yields a Peach-Koehler type force, which exhibits coupling of the applied loading to the history of the motion of the boundary velocity.