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首页> 外文会议>International Conference on Fracture and Strength of Solids >Anisotropic and isotropic elasticity, and its equivalence for singularity, interface and crack in bimateriais and trimaterials
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Anisotropic and isotropic elasticity, and its equivalence for singularity, interface and crack in bimateriais and trimaterials

机译：各向异性和各向同性的弹性，以及Bimateriais和Trimaterials的奇点，界面和裂缝等同物

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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：在本研究中研究了各向异性和各向同性弹性之间的等同性，在某些条件下进行二维变形。也就是说，当不同介质之间的界面沿着直线沿着直线呈现各向异性弹性的同一框架中，可以在各向异性弹性的相同框架中重建各向同性弹性。因此，即使对于双管材料，也可以将许多已知的各向异性自体物体的溶液视为有效的，其中一个或两个构成材料是各向同性的。等价的有用性是，可以容易地获得各向异性/各向同性自体化动物中的奇点和裂缝的溶液，而不会直接解决边界值问题。保护积分也具有各向异性和各向同性弹性之间的类似比较，使得J积分和J基相互积分M以相同的复合物形式表达，当积分路径的两个终点都处于直线接口时。分析延续和Schwarz-neumann的交替技术的方法应用于各向异性或各向同性的“微层”中的奇异性问题，其表示由沿两个平行接口粘合的三种不同材料组成的无限体。分析延续的方法替代地施加在两个平行界面上，以从相应的均匀溶液中以串联形式获得三层溶液。这里研究的微型解决方案可以应用于各种问题，例如，双层（包括半平面问题），半无限基板上的有限薄膜，以及薄膜的有限条带。提出了一些实施例以验证所得溶液的有用性。

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