Discontinuous quarter-point boundary elements revisited: Computation of T-stress in two-dimensional cracked components

Abstract

This paper analyzes the use of discontinuous quarter-point quadratic elements in a dual or hypersingular boundary element context to compute the T-stress for cracked 2-D isotropic components. The performance of this approach has been demonstrated in the past for stress intensity factors (SIFs) computation and, herein, it is revisited to assess its adequacy for T-stress evaluation. To this end, novel direct extrapolation formulas that determine the T-stress from the computed nodal displacements at the collocation nodes of the discontinuous quarter-point element are proposed, and their accuracy and effectiveness is satisfactorily tested by several numerical examples involving 2-D cracked Carbon NanoTube (CNT) reinforced composites. SIFs extrapolated from the computed nodal crack opening displacements and T-stress evaluated from the computed stresses at internal points (close to the crack-tip) are also presented for completeness. The proposed techniques are a valid and easy-to-implement alternative to the interaction integral approaches when determining SIFs and T-stress.