TY  - EJOU
AU  - Karlis, G.F.  
AU  - Tsinopoulos, S.V.  
AU  - Polyzos, D.  
AU  - Beskos, D.E.  

TI  - 2D and 3D Boundary Element Analysis of Mode-I Cracks in Gradient Elasticity
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2008
VL  - 26
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Boundary Elements
KW  -  fracture
KW  -  crack
KW  -  mode-I
KW  -  gradient elasticity

DO  - 10.3970/cmes.2008.026.189