The M waves emitted by an expanding phase boundary create a “lacuna”
The M waves emitted by an expanding phase boundary create a “lacuna”
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扩展相界发出的 M 波产生了“空隙”
DOI：
10.1115/1.4049222
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Markenscoff, Xanthippi
中科院分区：
文献类型：
--
作者：
Markenscoff, Xanthippi
Burridge 和 Willis 引入的 M 波（1969，“各向异性固体中扩展裂纹的自相似问题”，Math. Proc. Cambridge Philos. Soc.，66（2），第 443-468 页）由自相似扩展椭圆裂纹的表面发射，并以相应的裂纹速度发出瑞利波。在具有相变的自相似膨胀球形夹杂物（动态埃谢尔比问题）分析中，M波与基于动态格林函数得到的波有关，其中包含相不连续性扩展边界发射的最新小波的贡献，并且它们满足跨越不连续性移动相边界的相容性和线性动量的Hadamard跳跃条件。在膨胀包裹体的内部，它们通过抵消 P 和 S 的影响，创建了一个粒子速度为零的“空隙”。结果表明，“空隙”和 Eshelby 性质对于在不同粘度流体的自相似膨胀椭球区域中经历相变的牛顿流体也有效。
The M waves introduced by Burridge and Willis (1969, “The Self-Similar Problem of the Expanding Crack in an Anisotropic Solid,” Math. Proc. Cambridge Philos. Soc., 66(2), pp. 443–468) are emitted by the surface of a self-similarly expanding elliptical crack, and they give Rayleigh waves at the corresponding crack speed. In the analysis for the self-similarly expanding spherical inclusion with phase change (dynamic Eshelby problem), the M waves are related to the waves obtained on the basis of the dynamic Green’s function containing the contribution from the latest wavelets emitted by the expanding boundary of phase discontinuity, and they satisfy the Hadamard jump conditions for compatibility and linear momentum across the moving phase boundary of discontinuity. In the interior of the expanding inclusion, they create a “lacuna” with zero particle velocity by canceling the effect of the P and S. It is shown that the “lacuna” and Eshelby properties are also valid for a Newtonian fluid undergoing phase change in a self-similarly expanding ellipsoidal region of a fluid with different viscosity.