# On Singularities in 2D Linearized Elasticity

• Hiromichi Itou
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 26)

## Abstract

The aim of this paper is to introduce some convergent expansion formulae of solutions of two-dimensional linearized elasticity equation so-called as Navier’s equation around a crack tip and a tip of thin rigid inclusion, explicitly. In particular, three boundary value problems are treated; the first case is that a homogeneous and anisotropic body has a linear crack; the second case is that two different isotropic homogeneous bodies have an interfacial crack under the non-penetration condition and the frictional condition in Coulomb’s law; the third case is that a homogeneous and isotropic body has a rigid line inclusion. Moreover, the paper intends to clarify how the order of singularities in expansions is determined, which depends on the geometry of the material, the governing equation, boundary conditions, material properties, and so on.

## Notes

### Acknowledgments

H. Itou was partially supported by Grant-in-Aid for Scientific Research (C) (No. 26400178) of Japan Society for the Promotion of Science. I would like to thank M. Ikehata (Hiroshima University), V.A. Kovtunenko (University of Graz), A. Tani (Keio University), A.M. Khludnev and E.M. Rudoy (Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences) for the cooperation and fruitful discussions.

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