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首页> 外文期刊>Key Engineering Materials >Anisotropic and isotropic elasticity, and its equivalence for singularity, interface and crack in bimaterials and trimaterials
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Anisotropic and isotropic elasticity, and its equivalence for singularity, interface and crack in bimaterials and trimaterials

机译：双材料和三材料的各向异性和各向同性弹性及其等效性，用于奇异性，界面和裂纹

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摘要

The equivalence between anisotropic and isotropic elasticity is investigated in this study for two-dimensional deformation under certain conditions. That is, the isotropic elasticity can be reconstructed in the same framework of the anisotropic elasticity, when the interface between dissimilar media lies along a straight line. Therefore, many known solutions for an anisotropic bimaterial can be regarded as valid even for a bimaterial, in which one or both of the constituent materials are isotropic. The usefulness of the equivalence is that the solutions for singularities and cracks in an anisotropic/isotropic bimaterial can easily be obtained without solving the boundary value problems directly. Conservation integrals also have the similar analogy between anisotropic and isotropic elasticity so that J integral and J -based mutual integral M are expressed in the same complex forms for anisotropic and isotropic materials, when both end points of the integration paths are on the straight interface. The method of analytic continuation and Schwarz-Neumann's alternating technique are applied to singularity problems in an anisotropic or isotropic 'trimaterial', which denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. The method of analytic continuation is alternatively applied across the two parallel interfaces in order to derive the trimaterial solution in a series form from the corresponding homogeneous solution. The trimaterial solution studied here can be applied to a variety of problems, e.g. a bimaterial (including a half-plane problem), a finite thin film on semi-infinite substrate, and a finite strip of thin film, etc. Some examples are presented to verify the usefulness of the obtained solutions.
机译：在一定条件下，对于二维变形，研究了各向异性弹性和各向同性弹性的等效性。即，当异种介质之间的界面沿直线放置时，可以在各向异性弹性的相同框架内重建各向同性弹性。因此，即使对于其中一种或两种组成材料是各向同性的双材料，对于各向异性双材料的许多已知解决方案也可以被认为是有效的。等价的有用之处在于，可以在不直接解决边值问题的情况下轻松获得各向异性/各向同性双材料中的奇异点和裂纹的解决方案。守恒积分在各向异性弹性和各向同性弹性之间也具有相似的类比，因此当积分路径的两个端点都在直线界面上时，对于各向异性和各向同性材料，J积分和基于J的互积分M以相同的复数形式表示。解析连续法和Schwarz-Neumann交替技术应用于各向异性或各向同性的“三材料”中的奇异性问题，该奇异性问题表示由沿着两个平行界面结合的三种不同材料组成的无限体。替代地，将解析连续性方法应用于两个平行的界面，以便从相应的齐次溶液中导出系列形式的三材料溶液。本文研究的三材料解决方案可以应用于各种问题，例如一个双材料（包括一个半平面问题），一个半无限基片上的一个有限薄膜和一个有限的薄膜带等。给出了一些例子来验证所获得的解决方案的有效性。

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