Scaled boundary finite element method for calculating the J-integral based on LEFM

Abstract

The present study develops the scaled boundary finite element method (SBFEM) to derive the J-integral directly based on defining the rectangular contour. To achieve this, firstly the J-integral is calculated for each element with different path integrals of radial direction in an arbitrary subdomain. Then, the computed values of elements are summed in the entire domain. Finally, to validate and displaying the efficiency of the SBFEM solution, three two-dimensional (2D) numerical examples are solved for different integration paths. The results indicate path-independent property and fast convergency of this semi-analytical method in the term of J-integral computation.

Keywords:

• Scaled boundary finite element method (SBFEM)
• linear elastic fracture mechanics (LEFM)
• J-Integral
• two-dimensional (2D) problems
• rectangular contour
• path-independent integrals

Acknowledgments

The authors would like to acknowledge and express their special gratitude to anonymous reviewers, for their constructive comments that improved the quality of the manuscript.

Disclosure statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.