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Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity

Atroshchenko, Elena and Bordas, Stephane Pierre Alain 2015. Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2179) , 20150216. 10.1098/rspa.2015.0216

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Abstract

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Advanced Research Computing @ Cardiff (ARCCA)
Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Publisher: Royal Society of London
ISSN: 13645021
Last Modified: 11 Mar 2019 17:11
URI: http://orca-mwe.cf.ac.uk/id/eprint/92590

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