A sideface traction approach for cohesive and frictional crack growth problems using SBFEM

Abstract

This study develops a new procedure for solving cohesive and frictional crack growth problems in quasi-brittle materials such as concrete using the scaled boundary finite element method (SBFEM). In this procedure, the cohesive and contact tractions near the crack-tip region are modelled as linearised​ tractions on the ‘sidefaces’ of the cracked subdomains. The tractions away from the crack-tip region are implemented by utilising zero-thickness interface elements. A novel scheme is proposed to estimate the linearised sideface tractions in the cracked subdomain. The scheme utilises stress intensity factors (SIFs) iteratively within the load-step such that the crack-tip singularities vanish when the equilibrium position is reached. This leads to the stress fields in the crack-tip region being accurately captured without mesh refinement. A stress-based criterion is used to determine the crack propagation condition and direction, which requires minimal computational effort as the stresses in the crack-tip region are directly extracted from the semi-analytical formulation of SBFEM. The proposed method is versatile as it can solve both the cohesive and frictional crack growth problems. The efficacy of the method is shown through benchmark examples and practical applications.