Adaptive crack propagation analysis with the element‐free Galerkin method

Abstract

SUMMARYIn this paper, an adaptive analysis of crack propagation based on the error estimation by the elementfree Galerkin (EFG) method is presented. The adaptivity analysis in quasi-static crack propagation is achieved by adding and=or removing the nodes along the background integration cells, those are reÿned or recovered according to the estimated errors. These errors are obtained basically by calculating the di erence between the values of the projected stresses and original EFG stresses. To evaluate the performance of the proposed adaptive procedure, the crack propagation behaviour is investigated for several examples. The results of these examples show the e ciency and accuracy of the proposed scheme in crack propagation analysis.

MLS‐based variable‐node elements compatible with quadratic interpolation. Part II: application for finite crack element

“…The analytical solution of mode I stress intensity factor for such a configuration is given in References [35][36][37] as follows:…”

Meshless methods: A review and computer implementation aspects

“…[32] suggest a residual-based error estimator based on the difference between a recovered stress field and a raw EFG field, like in the well-known ZZ error estimator in the FEM [104]. This estimator is used in an adaptive method for static cracks in [33] and for propagating cracks in [69]. This estimator is also found in [67,68].…”

A ϑ method-based numerical simulation of crack growth in linear elastic fracture

“…The example was also tested in [11,12]. In those papers the authors referred to the analytical solution given by Tada et al in [13] which provides the mode I Stress Intensity Factor in function of the crack length in the form…”

“…In the presence of fatigue crack growth, the cracks are driven by the empirical Paris law [5] while, in general cases of monotonic loading, the crack increments are usually assigned after the determination of the crack growth direction. This approach is also used in the recent computational methods for LEFM like the extended finite element method (X-FEM) [8,9] and the meshless techniques based on the element-free Galerkin method (EFGM) [10,11,12].…”