Elastic symmetry with beachball pictures
Elastic symmetry with beachball pictures
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DOI：
10.1093/gji/ggab183
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发表时间：
2021-05
影响因子：
2.8
通讯作者：
W. Tape;C. Tape
中科院分区：
文献类型：
--
作者：
W. Tape;C. Tape
弹性映射或广义胡克定律将弹性材料中的应力与应变相关联。弹性贴图的对称性是指不更改贴图的材质重定向。我们从概念上和图像上讨论弹性对称性的问题。弹性映射被假定为线性的，我们研究它使用标准的概念，从线性代数，而不是张量代数。我们用地震学家熟悉的“海滩球”来描述应变和应力。弹性映射，其输入和输出是应变和应力，进而使用beachballs来描绘。我们能够推断出大多数弹性映射的对称性，有时仅仅通过检查它们的海滩球对称性。我们的许多结果都很熟悉，但我们的版本比文献中的版本更简单，更透明。
The elastic map, or generalized Hooke’s Law, associates stress with strain in an elastic material. A symmetry of the elastic map is a reorientation of the material that does not change the map. We treat the topic of elastic symmetry conceptually and pictorially. The elastic map is assumed to be linear, and we study it using standard notions from linear algebra—not tensor algebra. We depict strain and stress using the ‘beachballs’ familiar to seismologists. The elastic map, whose inputs and outputs are strains and stresses, is in turn depicted using beachballs. We are able to infer the symmetries for most elastic maps, sometimes just by inspection of their beachball depictions. Many of our results will be familiar, but our versions are simpler and more transparent than their counterparts in the literature.