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ARTICLE

2D and 3D Boundary Element Analysis of Mode-I Cracks in Gradient Elasticity

G.F. Karlis¹, S.V. Tsinopoulos², D. Polyzos³, D.E. Beskos⁴

1 Department of Mechanical and Aeronautical Engineering, University of Patras, GR- 26500 Patras, Greece
2 Department of Mechanical Engineering, Technological and Educational Institute of Patras, GR-26334, Patras, Greece
3 Department of Mechanical and Aeronautical Engineering, University of Patras, GR- 26500 Patras, Greece and Institute of Chemical Engineering and High Temperature Chemical Process, GR-26504, Patras, Greece
4 Department of Civil Engineering, University of Patras,GR-26500 Patras, Greece and Office of Theoretical and Applied Mechanics, Academy of Athens, GR-11527 Athens, Greece

Computer Modeling in Engineering & Sciences 2008, 26(3), 189-208. https://doi.org/10.3970/cmes.2008.026.189

Abstract

A boundary element method, suitable for solving two and three dimensional gradient elastic fracture mechanics problems under static loading, is presented. A simple gradient elastic theory (a simplied version of Mindlin's Form-II general theory of gradient elasticity) is employed and the static gradient elastic fundamental solution is used to construct the boundary integral representation of the problem with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well-posed problem. Surface quadratic line and quadrilateral boundary elements are employed for the two- and three dimensional case, respectively and the discretization is restricted only to the boundary. Two new special variable-order singularity discontinuous elements for two- and three-dimensional cases are proposed for the treatment of singular fields around the tip or the front of the crack and the numerical determination of the corresponding stress intensity factors (SIFs). Two numerical examples dealing with two- and three-dimensional mode-I cracks are presented and discussed.

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Keywords

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