BEM Solutions of Crack Problems in Gradient Elasticity

In this paper a boundary element method is used to solve gradient elastic fracture mechanics problems under static loading in three dimensions. A simplified version of Mindlinx2019;s Form II higher order gradient elastic theory is exploited and the Boundary Element Method (BEM), recently proposed by Polyzos et al. (2003) and Tsepoura et al. (2003), is utilized for the solution of Mode I gradient elastic problem. The Stress Intensity Factors (SIFs) are determined with the aid of a new special variable-order singularity discontinuous element applied at the tip of the crack. This element is designed to deal with fields that have different orders of singularities, as it is the case for displacement and traction fields in classical elastic case. Finally, a numerical example concerning the SIF calculation of a 3D mode I crack is presented.