Analysis for T-stress of cracks in 3D anisotropic elastic media by weakly singular integral equation method

• Published in: Computer methods in applied mechanics and engineering 2019-04, Vol.347, p.1004-1029
• Main Authors: Rungamornrat, Jaroon, Sukulthanasorn, Naruethep, Mear, Mark E.
• Format: Article
• Language: English
• Subjects: Anisotropic materials; BIEM; Boundary element method; Boundary integral method; Crack-face displacement; Cracks; Displacement; Domains; Elastic anisotropy; Elastic media; Galerkin method; Integral equations; Mathematical analysis; Singular integral equations; Solution space; T-stress; Weakly singular
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.01.007

This paper proposes an efficient numerical procedure for computing T-stresses of cracks in three-dimensional, linearly elastic, infinite media. The technique is established in a broad framework allowing a medium made of generally anisotropic materials and cracks of arbitrary shape and under general loading conditions to be treated. A pair of weakly singular, weak-form, displacement and traction boundary integral equations is utilized to formulate the key equations governing the unknown crack-face fields. Besides the basic benefits such as the reduction of spatial dimensions of the solution space and the efficient treatment of unbounded domains and remote boundary data, use of such integral equations in the formulation offers additional positive features including the computational simplicity resulting from the weakly singular nature of all involved integrals and the involvement of a complete set of crack-face displacement fields. A weakly singular symmetric Galerkin boundary element method together with the special near-front approximation is utilized to solve for the unknown relative crack-face displacement whereas the sum of the crack-face displacement is obtained from the displacement boundary integral equation for cracks via the Galerkin technique. The latter step is one of the essential aspects of the present study that provides the direct means for determining the T-stress data in terms of the sum of the crack-face displacement in the neighborhood of the crack-front. An extensive numerical study is conducted for various scenarios and a selected set of results is reported to demonstrate both the accuracy and capability of the proposed technique. •A numerical method is established to determine T-stress for cracks in 3D media.•The formulation is based on a pair of weakly singular weak-form integral equations.•A special element is used for the near-front relative crack-face displacement.•Explicit formulae are used to extract the T-stress from the crack-face data.•Highly accurate T-stress results are obtained using relatively coarse meshes.