Adaptive finite element analysis of mixed-mode crack problems with automatic mesh generator

Computing bounds to mixed-mode stress intensity factors in elasticity

“…In the following, the superscript * represents the results of SIFs obtained at crack tips based on fine mesh. Compared with the SIFs given in [15], K I = 0.2834, K II = 0.6228 at crack tip A, and K I = 0.2047, K II = 0.6586 at crack tip B, the relative differences are respectively 0.2834−0.2765 0.2834 = 2.44% and 2.12% for K I and K II at crack tip A, 4.05% and 1.17% for K I and K II at crack tip B. According to the relative differences, it can be seen that these results obtained from the fine mesh are in the limit of acceptance.…”

A gradient‐based adaptation procedure and its implementation in the element‐free Galerkin method

“…In the gradient-based methods, the reÿnement-coarsening criterion is based on the assumption: a larger gradient needs a richer mesh and vice versa. The validity of this assumption can be justiÿed by observing numerical results from a large quantity of literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], adapted meshes are usually denser in areas with a higher variation of strains or stresses; on the other hand, a coarser mesh may not be able to produce accurate displacements or stresses, but might give an adequate information about how these ÿelds vary in the problem domain. As regard to which ÿeld should be considered, there are quite several choices: displacement, strain, stress and so on.…”

“…the ÿnite element methods and the meshless methods, mesh reÿnement based on an adaptation mechanism is becoming a standard procedure, in order to achieve a prescribed accuracy with a minimal number of nodes or to capture a local structural behavior. Most adaptation methods [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] were developed aiming at ÿnite element methods, and it is for this reason some of them have limitations or are inconvenient in application to meshless methods. For example, the popular ZZ method [12,13] requires knowing optimal or superconvergent points which are usually coincident with Gaussian points in elements.…”

An extended cohesive damage model for simulating arbitrary damage propagation in engineering materials

“…Modelling arbitrary discontinuities and their propagation is currently one of the major concerns in the fracture related academic community. One of the earliest techniques used to model such discontinuities is Adaptive Mesh Refining (AMR) scheme which was developed between 1987 and 2000 [1,2]. In AMR, a finite element mesh can be adaptively modified according to crack propagation, and errors during numerical simulation can be efficiently minimized.…”