Self-similarly expanding regions of phase change yield cavitational instabilities and model deep earthquakes
Self-similarly expanding regions of phase change yield cavitational instabilities and model deep earthquakes
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DOI：
10.1016/j.jmps.2019.02.017
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发表时间：
2019-06
影响因子：
5.3
通讯作者：
X. Markenscoff
中科院分区：
文献类型：
--
作者：
X. Markenscoff
从在预应力下经历相变（密度变化，即体积塌陷和模量变化）的自相似膨胀椭球体区域发出的动力场构成了开创性的埃谢尔比不均匀性问题（作为等效包含问题）的动态推广，它们由膨胀椭球体表面发出的压力、剪切和M波以及在裂纹极限下产生的瑞利波组成。它们可能构成了在非常高的压力下和由于相变而发生的深焦点地震（DFE）的模型。物理学的两个基本定理支配着这一现象：柯西-科瓦勒夫斯卡亚定理，仅基于维度分析和解析性质，规定内部粒子速度为零；诺特定理，将移动相界所花费的能量极端化（为了稳定而最小化），使其不会成为能量的汇（或源），并确定自相似形状（轴膨胀速度）。诺特定理的表达式表明，膨胀区域可以是平面的，从而打破了输入的对称性，这种现象表现为一种新发现的“动态塌陷/空化不稳定性”，其中凝聚在非常薄的区域中的非常大的应变能可以逸出。在存在剪切的情况下，扁平的非常薄的椭球体（或带）将在空间中定向，以便预应力下相变产生的能量能够以最小的损失逸出，凝聚在位错核心中，在施加最大构型力（Peach-Koehler）的平面上滑出。平面发生的相变会在扁平的膨胀椭圆体中产生，这是 DFE 中存在的一种新缺陷。辐射图是根据相变六个本征应变分量的等效值获得的，其中还包含由于扁平椭球体的动态埃谢尔比张量的平面性而产生的影响。 DFE文献中的一些模型是在不具有移动相不连续边界的能量的基础上进行评估和排除的。诺特定理在各向异性和非线性弹性方面是有效的，并且该现象与尺度无关，从纳米到非常大的尺度都有效，并且普遍适用于应力引起的马氏体转变、剪切带和非晶化的其他动态现象。
The dynamical fields that emanate from self-similarly expanding ellipsoidal regions undergoing phase change (change in density, i.e., volume collapse, and change in moduli) under pre-stress, constitute the dynamic generalization of the seminal Eshelby inhomogeneity problem (as an equivalent inclusion problem), and they consist of pressure, shear, andMwaves emitted by the surface of the expanding ellipsoid and yielding Rayleigh waves in the crack limit. They may constitute the model of Deep Focus Earthquakes (DFEs) occurring under very high pressures and due to phase change. Two fundamental theorems of physics govern the phenomenon: the Cauchy-Kowalewskaya theorem, which, based on dimensional analysis and analytic properties alone, dictates that there is zero particle velocity in the interior, and Noether's theorem, that extremizes (minimizes for stability) the energy spent to move the phase boundary so that it does not become a sink (or source) of energy, and which determines the self-similar shape (axes expansion speeds). The expression from Noether's theorem indicates that the expanding region can beplanar, thusbreaking the symmetryof the input and the phenomenon manifests itself as a newly discovered one of a “dynamic collapse/ cavitation instability”, where very large strain energy condensed in the very thin region can escape out. In the presence of shear, the flattened very thin ellipsoid (or band) will be oriented in space so that the energy due to phase change under pre-stress is able to escape out at minimum loss condensed in the core of dislocations gliding out on the planes where the maximum configurational force (Peach-Koehler) is applied on them. Phase change occurring planarly produces in a flattened expanding ellipdoid, a new defect present in the DFEs. The radiation patterns are obtained in terms of the equivalent to the phase change six eigenstrain components, which also contain effects due to planarity through the Dynamic Eshelby Tensor for the flattened ellipsoid. Some models in the literature of DFEs are evaluated and excluded on the basis of not having the energy to move the boundary of phase discontinuity. Noether's theorem is valid in anisotropy and nonlinear elasticity, and the phenomenon is independent of scales, valid from the nano to the very large ones, and applicable in general to other dynamic phenomena of stress induced martensitic transformations, shear banding, and amorphization.