Stabilization of notched elements' fracture by using a control algorithm

Abstract

Crack propagation is a significant mechanism for quasi-brittle materials under applied loading. It can occur very suddenly and causes numerical instabilities and deficiencies in some problems. This behavior manifest itself as non-convergence solutions i.e. the inability to obtain the entire load-displacement curve or jumps in the load displacement curve. In this study, a control technique is implemented to obtain the whole load–displacement curve when crack propagation causes severe numerical instabilities such as snap-back behavior. The performance of the control technique was demonstrated by simulating uniaxial tension test of pre-notched plate, three-point bending test of a notched beam and mixed-mode test of a notched plate. This study shows that the control algorithm is able to produce a stable solution path for these kinds of problems. This method can be easily implemented in available commercial finite element codes without the need for any user defined subroutines.