Crack Growth Prediction by Manifold Method
Publication: Journal of Engineering Mechanics
Volume 125, Issue 8
Abstract
The prediction of crack growth is studied by the manifold method. The manifold method is a new numerical method proposed by Shi. This method provides a unified framework for solving problems dealing with both continuums and jointed materials. It can be considered as a generalized finite-element method and discontinuous deformation analysis. One of the most innovative features of the method is that it employs both a physical mesh and a mathematical mesh to formulate the physical problem. The physical mesh is dictated by the physical boundary of a problem, while the mathematical mesh is dictated by the computational consideration. These two meshes are interrelated through the application of weighting functions. In this study, a local mesh refinement and auto-remeshing schemes are proposed to extend the manifold method. The proposed model is first verified by comparing the numerical results with the benchmark solutions, and the results show satisfactory accuracy. The crack growth problems and the stress distributions are then investigated. The manifold method is proposed as an attractively new numerical technique for fracture mechanics analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Arrea, A., and Ingraffea, A. R. (1982). “Mixed-mode crack propagation in mortar and concrete.” Rep. No. 81-13, Cornell University, Ithaca, N.Y.
2.
Belytschko, T., Lu, Y. Y., and Gu, L. (1994). “Element-free Galerkin methods.” Int. J. Numer. Methods in Engrg., 37, 229–256.
3.
Belytschko, T., Lu, Y. Y., and Gu, L. (1995a). “Crack propagation by element-free Galerkin methods.” Engrg. Fracture Mech., 51, 295–315.
4.
Belytschko, T., Lu, Y. Y., Gu, L., and Tabbara, M. (1995b). “Element-free Galerkin methods for static and dynamic fracture.” Int. J. Solids and Struct., 32, 2547–2570.
5.
Bittencourt, T. N., Warrzynek, P. A., Ingraffea, A. R., and Sousa, J. L. (1996). “Quasi-automatic simulation of crack propagation for 2D LEFM problems.” Engrg. Fracture Mech., 55, 321–334.
6.
Cain, G. L. (1994). Introduction to general topology. Addison-Wesley, Reading, Mass.
7.
Chai, G., Zhang, K., and Wu, D. (1995). “Stress intensity factors for semi-elliptical surface cracks in plates and cylindrical pressure vessels using the hybrid boundary element method.” Engrg. Fracture Mech., 52, 1035–1054.
8.
Chen, G., Ohnishi, Y., and Ito, T. (1998). “Development of high-order manifold method.” Int. J. Numer. Methods in Engrg., 43, 685–712.
9.
Erdogan, F., and Sih, S. C. (1963). “On the crack extension in plates under plane loading and transverse shear.” J. Basic Engrg., 85, 519–525.
10.
Lim, I. L., Johnston, I. W., and Choi, S. K. (1996). “A finite element code for fracture propagation analysis within elasto-plastic continuum.” Engrg. Fracture Mech., 53, 193–211.
11.
Lu, Y. Y., Belytschko, T., and Tabbara, M. (1995). “Element-free Galerkin method for wave propagation and dynamic fracture.” Comp. Method Application to Mech. Engrg., 126, 131–153.
12.
Nayroles, B., Touzot, G., and Villon, P. (1992). “Generalizing the finite element method: Diffuse approximation and diffuse elements.” Computational Mech., 10, 307–318.
13.
Paris, P. C., and Sih, G. C. (1965). “Stress analysis of cracks.” ASTM STP, 381, 1–30.
14.
Raveendra, S. T., and Banerjee, P. K. (1991). “Computation of stress intensity factors for interfacial cracks.” Engrg. Fracture Mech., 40(1), 89–103.
15.
Raveendra, S. T., and Banerjee, P. K. (1992). “Boundary element analysis of cracks in thermally stressed planar structures.” Int. J. Solids and Struct., 29(18), 2301–2317.
16.
Shi, G. H. ( 1988). “Discontinuous deformation analysis: A new numerical method for the static and dynamics of block systems,” PhD dissertation, Dept. of Civ. Engrg., University of California, Berkeley, Calif.
17.
Shi, G. H. (1995). “Numerical manifold method.” Working Forum on the Manifold Method of Mat. Anal., 1–180.
18.
Sih, G. C. (1974). “Strain-energy-density factor applied to mixed crack problems.” Int. J. Fracture, 10(3), 305–321.
19.
Tada, H., Paris, P. C., and Irwin, G. R. (1973). The stress analysis of cracks handbook. Del Research Corp., Hellertown, Pa.
20.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity, 3rd Ed., McGraw-Hill, New York.
21.
Xie, M., Gerstle, W. H., and Rahulkumar, P. (1995). “Energy-based automatic mixed-mode crack-propagation modeling.”J. Engrg. Mech., ASCE, 121(8), 914–923.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 125 • Issue 8 • August 1999
Pages: 884 - 890
History
Received: Jul 9, 1998
Published online: Aug 1, 1999
Published in print: Aug 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.