A problem of anisotropic/isotropic bimaterial with a singularity or under a remote stress

초록

The analysis of the stresses and displacements in thin film/substrate is usually carried out assuming both materials (film & substrate) are isotropic or anisotropic. However, there often exists a bimaterial system comprising an isotropic film on an anisotropic substrate (or vice versa). With a view to analyzing the bimaterial system of isotropic film/anisotropic substrate (or vice versa), a method to obtain the solution for this system (but both materials are semi-infinite) is presented. It is found that the stresses and the displacements in isotropic material can be written in almost the same form as in anisotropic material, and moreover, they are expressed in a form identical to that of anisotropic material when x(2)=0, the interface. This makes it possible to obtain the solution for isotropic/anisotropic bimaterial under remote stress (or due to a singularity lying in either material) if the solution is known for anisotropic/anisotropic bimaterial with otherwise the same conditions. Two exemplary problems are solved; one is isotropic/anisotropic bimaterial (infinite) under a remote stress, and the other, isotropic/anisotropic bimaterial (infinite) due to a point force in either material. The solution for the latter case is verified against the result from FEM, in which a glass is selected as an isotropic material with Si chosen as an anisotropic material. A further study to apply the present method to a thin film (finite thickness)/substrate (semi-infinite) bimaterial system is needed, and now in progress.

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