Fast and accurate numerical solution to an elastostatic problem involving ten thousand randomly oriented cracks
Source abstract
Abstract
An algorithm is presented for the multiple crack problem in planar linear elastostatics. The algorithm has three important properties: it is stable, it is adaptive, and its complexity is linear. This means that high accuracy can be achieved and that large-scale problems can be treated. In a numerical example stress fields are accurately computed in a mechanically loaded material containing 10,000 randomly oriented cracks. The computing time is about two and a half hours on a regular workstation.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Electromagnetic Scattering and Analysis · Numerical methods in engineering · Advanced Numerical Methods in Computational Mathematics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (17)
Show source-provided references
1. Brencich, A. and Carpinteri, A. (1996). Interaction of a main crack with ordered distribution of microcracks: a numerical technique by displacement discontinuity boundary elements. International Journal of Fracture 76, 373-389.10.1007/BF00039784 ↗
2. Carrier, J., Greengard, L. and Rokhlin, V. (1988). A fast adaptive multipole algorithm for particle simulations. SIAM Journal on Scientific and Statistical Computing 9, 669-686.10.1137/0909044 ↗
3. Chang, C. and Mear, M.E. (1995). A boundary element method for two dimensional linear elastic analysis. International Journal of Fracture 74, 219-251.10.1007/BF00033829 ↗
4. Chen, Y.Z. (1997). Numerical solution of multiple crack problem using hypersingular integral equation. International Journal of Fracture 88, L9-L14.
5. Freij-Ayoub, R., Dyskin, A.V. and Galybin, A.N. (1997). The dislocation approximation for calculating crack interaction. International Journal of Fracture 86, L57-L62.
6. Greengard, L. and Helsing, J. (1998). On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites. Journal of the Mechanics and Physics of Solids 46, 1441-1462.10.1016/S0022-5096(97)00041-0 ↗
7. Greengard, L. and Rokhlin, V. (1987). A fast algorithm for particle simulations. Journal of Computational Physics 73, 325-348.10.1016/0021-9991(87)90140-9 ↗
8. Helsing, J. (1996). Thin bridges in isotropic electrostatics. Journal of Computational Physics 127, 142-151.10.1006/jcph.1996.0164 ↗
9. Helsing, J. and Peters, G. (1999). Integral equation methods and numerical solutions of crack and inclusion problems in planar elastostatics. SIAM Journal on Applied Mathematics 59, 965-982.
10. Muskhelishvili, N.I. (1953). Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff Ltd, Groningen.
11. Pan, E. (1997). A general boundary element analysis of 2-D linear elastic fracture mechanics. International Journal of Fracture 88, 41-59.10.1023/A:1007462319811 ↗
12. Rokhlin, V. (1985). Rapid solution of integral equations of classical potential theory. Journal of Computational Physics 60, 187-207.10.1016/0021-9991(85)90002-6 ↗
13. Saad, Y. and Schultz, M.H. (1986). GMRES: a generalized minimum residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 7, 856-869.10.1137/0907058 ↗
14. Theocaris, P.S. and Ioakimidis, N.I. (1977). The inclusion problem in plane elasticity. Quarterly Journal of Mechanics and Applied Mathematics 30, 437-448.10.1093/qjmam/30.4.437 ↗
15. Wang, Y.B. and Chau, K.T. (1997). A new boundary element for plane elastic problems involving cracks and holes. International Journal of Fracture 87, 1-20.10.1023/A:1007469816603 ↗
16. Xueli, H. and Tzuchiang, W. (1996a). A general method for solving the problem of both open and closed multiple cracks. International Journal of Fracture 79, R69-R72.10.1007/BF00018603 ↗
17. Xueli, H. and Tzuchiang, W. (1996b). Interacting multiple cracks with complicated crack surface conditions. International Journal of Fracture 82, R53-R57.10.1007/BF00013166 ↗