Matched interface and boundary method for elasticity interface problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:285

Article

Wang, Bao¹  Xia, Kelin¹  Wei, Guo-Wei^1,2 

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Michigan State Univ, Dept Elect & Comp Engn, E Lansing, MI 48824 USA

关键词: Elasticity equations;    Elasticity interface problems;    Spatial-dependent shear modulus;    Matched interface and boundary;   

DOI  :  10.1016/j.cam.2015.02.005

来源: Elsevier

【 摘 要 】

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquitous in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lame's parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L-infinity and L-2 norms. (C) 2015 Elsevier B.V. All rights reserved.

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