Open AccessAn interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method
Author(s) -
Nha Thanh Nguyen,
Hien Thai Nguyen,
Minh Ngoc Nguyen,
Thanh-Dat Truong
Publication year - 2015
Publication title -
khoa học công nghệ
Language(s) - English
Resource type - Journals
ISSN - 1859-0128
DOI - 10.32508/stdj.v18i2.1079
Subject(s) - kronecker delta , interpolation (computer graphics) , stress field , mathematics , series (stratigraphy) , stress intensity factor , mathematical analysis , point (geometry) , field (mathematics) , fracture mechanics , fracture (geology) , stress (linguistics) , function (biology) , series expansion , geometry , structural engineering , physics , finite element method , classical mechanics , pure mathematics , materials science , engineering , geology , motion (physics) , philosophy , linguistics , composite material , biology , paleontology , quantum mechanics , evolutionary biology
The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.