Finite Element with Inner Softening Band
Publication: Journal of Engineering Mechanics
Volume 117, Issue 3
Abstract
A new technique for modeling localized deformations within a softening band is described, where softening is attributed to a displacement discontinuity within an element. Concepts such as fracture strain are not included in the formulation of the model, and consequently nonlocal parameters such as internal length measures are not needed. It is shown that the shape functions within the element provide the necessary information normally given with internal length. In this manner, objectivity with regard to element configuration seems to be automatically satisfied, which is demonstrated by numerical studies in which Rankine failure criterion is employed. It is also noted that the displacement field rather than the strain field is additively decomposed into elastic and inelastic parts. This additivity is valid independently of the magnitude of displacement continuity in the softening band, which implies that the technique can be extended in a straight‐forward fashion to finite displacements.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bažant, Z. P. (1986). “Mechanics of distributed cracking.” Appl. Mech. Revue, 39, 675–705.
2.
Belytschko, T., Fish, J., and Engelmann, B. E. (1988). “A finite element with embedded localization zones.” J. Comp. Methods Appl. Mech. Engrg., 70, 59–89.
3.
Dahlblom, O., and Ottosen, N. (1990). “Smeared crack analysis using a generalized fictitious crack model.” J. Engrg. Mech., ASCE, 116, 55–76.
4.
Fish, J., and Belytschko, T. (1988). “Elements with embedded localization zones.” J. Comp. and Structures, 30, 247–256.
5.
Hillerborg, A., Modeer, M., and Peterson, P. L. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cement and Concrete Res., 6, 773–782.
6.
Nilsson, L., and Oldenburg, M. (1983). “Nonlinear wave propagation in plastic fracturing materials.” IUTAM Symp., Nonlinear Waves, Springer Verlag, Berlin, 209–217.
7.
Ortiz, M., Leroy, Y., and Needlemann, A. (1987). “A finite element method for localized failure analysis.” J. Comp. Methods Appl. Mech. Engrg., 61, 189–214.
8.
Pietruszczak, S., and Mroz, Z. (1981). “Finite element analysis of deformation of strain‐softening materials.” Int. J. Num. Methods Engrg., 17, 327–334.
9.
Pramono, E., and Willam, K. J. (1989). “Fracture energy‐based plasticity formulation of plain concrete.” J. Engrg. Mech., ASCE, 115(6), 1183–1204.
10.
Willam, K. J., Bicanic, N., and Sture, S. (1984). “Constitutive and computational aspects of strain softening and localization in solids.” ASME/WAM 1984 Symp. on Constitutive Equations, Macro‐ and Computational Aspects, American Society of Mechanical Engineering, G00274, 233–252.
Information & Authors
Information
Published In
Copyright
Copyright © 1991 ASCE.
History
Published online: Mar 1, 1991
Published in print: Mar 1991
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.