Reference : Fundamental solutions and dual boundary element methods for fracture in plane Cossera...
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
http://hdl.handle.net/10993/34896
Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity
English
Atroshchenko, Elena [> >]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit]
2015
Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences
471
2179
Yes (verified by ORBilu)
International
1364-5021
[en] boundary element method ; crack problem ; Cosserat elasticity ; fracture
[en] 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.
Fondecyt Chile grant no. 11130259 entitled ‘Boundary element modelling of crack propagation in micropolar materials’.
Researchers ; Professionals ; Students ; General public ; Others
http://hdl.handle.net/10993/34896
10.1098/rspa.2015.0216
FP7 ; 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery

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