Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis

A finite element method, with the adaptive Delaunay triangulation as mesh generator, is used to analyze two-dimensional crack propagation problems. This paper describes the Delaunay triangulation procedure consisting of mesh generation, node creation, mesh smoothing, and adaptive remeshing, all with object-oriented programming. The adaptive remeshing technique generates small elements around crack tips and large elements in other regions. The resulting stress intensity factors and simulated crack propagation behavior are used to evaluate the effectiveness of the combined method. The accuracy of the stress intensity factor prediction is evaluated in three test cases, a center cracked plate, a single edge cracked plate and a compact tension specimen. Then, crack growth trajectories in a single edge cracked plate with three holes and a single edge cracked plate under mixed-mode loading are simulated and results assessed.

[1]  Jaime Planas,et al.  KI evaluation by the displacement extrapolation technique , 2000 .

[2]  Paul-Louis George,et al.  ASPECTS OF 2-D DELAUNAY MESH GENERATION , 1997 .

[3]  R. Barsoum.  Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements , 1977 .

[4]  Paul A. Wawrzynek,et al.  Quasi-automatic simulation of crack propagation for 2D LEFM problems , 1996 .

[5]  B. K. Karamete,et al.  UNSTRUCTURED GRID GENERATION AND A SIMPLE TRIANGULATION ALGORITHM FOR ARBITRARY 2-D GEOMETRIES USING OBJECT ORIENTED PROGRAMMING , 1997 .

[6]  Y. Murakami.  Stress Intensity Factors Handbook , 2006 .

[7]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[8]  D. M. Parks.  A stiffness derivative finite element technique for determination of crack tip stress intensity factors , 1974 .

[9]  P. Dechaumphai.  Improvement of plane stress solutions using adaptive finite elements , 1996 .

[10]  W. Frey.  Selective refinement: A new strategy for automatic node placement in graded triangular meshes , 1987 .

[11]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[12]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[13]  R. Barsoum.  On the use of isoparametric finite elements in linear fracture mechanics , 1976 .

[14]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[15]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[16]  M. Isida.  Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions , 1971 .

[17]  N. Weatherill,et al.  Efficient three‐dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints , 1994 .

[18]  G. Sih.  Strain-energy-density factor applied to mixed mode crack problems , 1974 .

[19]  S. Sloan.  A fast algorithm for generating constrained delaunay triangulations , 1993 .

[20]  Herbert A. Mang,et al.  The Fifth World Congress on Computational Mechanics , 2002 .

[21]  S. Chan,et al.  On the Finite Element Method in Linear Fracture Mechanics , 1970 .

[22]  S. Rahman,et al.  An efficient meshless method for fracture analysis of cracks , 2000 .

[23]  Paul A. Wawrzynek,et al.  An algorithm to generate quadrilateral or triangular element surface meshes in arbitrary domains with applications to crack propagation , 1995 .

[24]  R. Nuismer.  An energy release rate criterion for mixed mode fracture , 1975 .

[25]  B. Moran,et al.  A general treatment of crack tip contour integrals , 1987 .