Journal article
Eigenfunctions of the 2-dimensional anisotropic elasticity operator and algebraic equivalent materials
Publication Details
Authors: | Specovius-Neugebauer, M.; Steigemann, M. |
Publication year: | 2008 |
Journal: | Journal of Applied Mathematics and Mechanics |
Pages range : | 100-115 |
Journal acronym: | ZAMM |
Volume number: | 88 |
Start page: | 100 |
End page: | 115 |
ISSN: | 0044-2267 |
eISSN: | 1521-4001 |
DOI-Link der Erstveröffentlichung: |
Abstract
The displacement field of an elastic anisotropic solid with a crack has an asymptotic expansion near the crack tip in terms of special solutions of the homogeneous elasticity problem in the whole plane with a semi-infinite crack. These so-called eigenfunctions of the elasticity operator and their coefficients play an essential role in the determination of crack paths. Eigenfunctions are exactly known for isotropic solids, but not for anisotropic ones. Using the concept of algebraically equivalent materials, analytical expressions of the eigenfunctions can be presented for all classes of anisotropic materials which are algebraically equivalent to isotropic materials. The paper contains a complete characterization of these materials. For arbitrary materials, the polynomial eigenfunctions are found analytically, while for the remaining eigenfunctions a simple and efficient method is presented for the numerical computation. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
The displacement field of an elastic anisotropic solid with a crack has an asymptotic expansion near the crack tip in terms of special solutions of the homogeneous elasticity problem in the whole plane with a semi-infinite crack. These so-called eigenfunctions of the elasticity operator and their coefficients play an essential role in the determination of crack paths. Eigenfunctions are exactly known for isotropic solids, but not for anisotropic ones. Using the concept of algebraically equivalent materials, analytical expressions of the eigenfunctions can be presented for all classes of anisotropic materials which are algebraically equivalent to isotropic materials. The paper contains a complete characterization of these materials. For arbitrary materials, the polynomial eigenfunctions are found analytically, while for the remaining eigenfunctions a simple and efficient method is presented for the numerical computation. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
