An element‐free Galerkin method for 3D crack propagation simulation under complicated stress conditions

Abstract

SUMMARY This study develops an element‐free Galerkin method based on the moving least‐squares approximation to trace three‐dimensional crack propagation under complicated stress conditions. The crack surfaces are modelled by a collection of planar triangles that are added when cracks propagate. The visibility criterion is adopted to treat the screening effect of the cracks on the influenced domain of a Gaussian point. Cracks are assumed to propagate in the perpendicular planes at crack front points when the strain energy release rates reach the material fracture toughness. This method is unique in that it uses a nonlinear contact iterative algorithm to consider contributions of crack surface interaction to the global equilibrium equations, so that crack opening, sliding and closing under complicated stress states can be efficiently modelled. Two numerical examples of three‐dimensional quasi‐static crack propagation were modelled with satisfactory results. Copyright © 2012 John Wiley & Sons, Ltd.

An adaptive cracking particle method providing explicit and accurate description of 3D crack surfaces

“…In the aforementioned work, a curvilinear coordinate system is used for 3D cracks with curved and nonplanar surfaces. Since flat triangular meshes are used here to model crack surfaces, integrating over a cube with a Cartesian coordinate system is appropriate and keeps the calculation simple …”

“…Since flat triangular meshes are used here to model crack surfaces, integrating over a cube with a Cartesian coordinate system is appropriate and keeps the calculation simple. 9,26,27,62 A local coordinate system as shown in Figure 8 is used…”

Influence of Weight-Functions on the Performance of Element-Free Galerkin Method

“…The attractive feature of element free Galerkin method is high rate of convergence if appropriate weight function is selected. Element free Galerkin method is very popular for solving problems such as fracture mechanics [17,18,19], wave and crack propagation [20,21,22], composite damage [23,24], electromegntic fields [25,26], metal forming & welding [27,28], fluid dynamics & heat transfer [29,30] and medical field [31].…”

Consistent element‐free Galerkin method

“…So far, EFG is still one of the most popular and successful meshfree methods, and its recent progress can be found in various applications such as free surface flow , 3D crack propagation , and large‐scale simulations and so on. The fundamental advantage of EFG against the traditional FEM is the smoothness of the approximation function.…”

“…Numerical results show that the proposed CEFG method greatly improves the numerical performance of the EFG method in terms of accuracy, convergence, efficiency and stability, especially the proposed cubic CEFG method, which shows exceptional accuracy and convergence. by these meshfree methods is that they are based on scattered data approximation techniques, which do not need explicit nodal connectivity to construct elements.So far, EFG is still one of the most popular and successful meshfree methods, and its recent progress can be found in various applications such as free surface flow [6], 3D crack propagation [7], and large-scale simulations [8] and so on. The fundamental advantage of EFG against the traditional FEM is the smoothness of the approximation function.…”