Browse > Article

Adaptive Mesh Refinement Procedure for Shear Localization Problems  

Kim, Hyun-Gyu (Department of Mechanical Engineering, Seoul National University of Technology)
Im, Se-Young (Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology)
Publication Information
Journal of Mechanical Science and Technology / v.20, no.12, 2006 , pp. 2189-2196 More about this Journal
Abstract
The present work is concerned with the development of a procedure for adaptive computations of shear localization problems. The maximum jump of equivalent strain rates across element boundaries is proposed as a simple error indicator based on interpolation errors, and successfully implemented in the adaptive mesh refinement scheme. The time step is controlled by using a parameter related to the Lipschitz constant, and state variables in target elements for refinements are transferred by $L_2$-projection. Consistent tangent moduli with a proper updating scheme for state variables are used to improve the numerical stability in the formation of shear bands. It is observed that the present adaptive mesh refinement procedure shows an excellent performance in the simulation of shear localization problems.
Keywords
Finite Elements; Error Indicator; Mesh Refinement; Adaptivity; Shear Localization;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 Zhu, J. Z., 1997, 'A Posteriori Error Estimation - The Relation Between Different Procedures,' Computer Methods in Applied Mechanics and Engineering, Vol. 150, pp. 411-422   DOI   ScienceOn
2 Zienkiewicz, O. C. and Zhu, J. Z., 1991, 'Adaptivity and Mesh Generation,' International Journal for Numerical Methods in Engineering, Vol. 32, pp. 783-810   DOI
3 Zienkiewicz, O. C. and Zhu, J. Z., 1992, 'The Super-convergent Patch Recovery and a Posteriori Error-estimates, Part I: The Recovery Technique,' International Journal for Numerical Methods in Engineering, Vol. 33, pp. 1331-1364   DOI
4 Ciarlet, P. G., 1978, The Finite Element Method for Elliptic Problems, North-Holland
5 Demkowicz, L., Devloo, P. and Oden, J. T., 1985, 'On an Hr-type Mesh-refinement Strategy ？Based on Minimization of Interpolation Errors,' Computer Methods in Applied Mechanics and Engineering, Vol. 53, pp. 67-89   DOI   ScienceOn
6 Khoei, A. R. and Lewis, R. W., 2002, 'H-adaptive Finite Element Analysis for Localization Phenomena with Reference to Metal Powder Forming,' Finite Elements in Analysis and Design, Vol. 38, pp. 503-519   DOI   ScienceOn
7 Kim, H. -G. and Im, S., 1999, 'Approximate Analysis for Shear Band in a Thermoviscoplastic Material,' ASME Journal of Applied Mechanics, Vol. 66, pp.687-694   DOI
8 Lemonds, J. and Needleman, A., 1986, 'Finite Element Analyses of Shear Localization in Rate and Temperature Dependent Solids,' Mechanics of Materials, Vol. 5, pp. 339-361   DOI   ScienceOn
9 Lush, A. M., Weber, G. and Anand, L., 1989, 'An Implicit Time-integration Procedure for a Set of Internal Variable Constitutive Equations for Isotropic Elasto-viscoplasticity,' International Journal of Plasticity, Vol. 5, pp. 521-549   DOI   ScienceOn
10 Ortiz, M. and Quigley, J. J., 1991, 'Adaptive Mesh Refinement in Strain Localization Problems,' Computer Methods in Applied Mechanics and Engineering, Vol. 90, pp. 781-804   DOI   ScienceOn
11 Peirce, D., Shih, C. F. and Needleman, A., 1984, 'A Tangent Modulus Method for Rate Dependent Solids,' Computers & Structures, Vol. 18, pp. 875-887   DOI   ScienceOn
12 Peric, D., Hochard, c., Dutko, M. and Owen, D. R. J., 1996, 'Transfer Operators for Evolving Meshes in Small Strain Elasto-plasticity,' Computer Methods in Applied Mechanics and Engineering, Vol. 137, pp. 331-344   DOI   ScienceOn
13 Aiken, R. C., 1985, Stiff Computation, Oxford University Express
14 Babuska, I. and Rheinboldt, W. C., 1978, 'Error Estimates for Adaptive Finite Element Computations,' SIAM Journal of Numerical Analysis, Vol. 15, pp. 736-754   DOI   ScienceOn
15 Batra, R. C. and Ko, K. I., 1992, An Adaptive Mesh Refinement Technique for the Analysis of Shear Bands in Plane Strain Compression of a Thermoviscoplastic Solid,' Computational Mechanics, Vol. 10, pp. 369-379   DOI
16 Belytschko, T. and Tabbara, M., 1993, 'Hadaptive Finite Element Methods for Dynamic Problems, with Emphasis on Localization,' International Journal for Numerical Methods in Engineering, Vol. 36, pp. 4245-4265   DOI   ScienceOn
17 Belytschko, T., Chiang, H. Y. and Plaskacz, E., 1994, 'High Resolution Two-dimensional Shear Band Computations: Imperfections and Mesh Dependence,' Computer Methods in Applied Mechanics and Engineering, Vol. 119, pp.1-15   DOI   ScienceOn