TECHNICAL PAPERS
Aug 1, 1998

Analysis of Rotating Crack Model

Publication: Journal of Engineering Mechanics
Volume 124, Issue 8

Abstract

This paper extends the standard rotating crack (RC) model to a formulation with multiple orthogonal cracks. The corresponding stress evaluation algorithm is described, and a derivation of the tangent stiffness matrix is presented. The derivation is extended to the case of equal principal strains, in which the classical formula for the tangent shear modulus fails. A condition excluding snapback of the stress-strain diagram for an arbitrary loading path is derived. Attention then shifts to stress locking, meaning here spurious stress transfer across widely opening cracks. The problem is illustrated by numerical examples. The mechanism of stress transfer is thoroughly analyzed, and the source of locking is detected. A remedy and extension of the model to a nonlocal formulation is described in a separate paper.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Arrea, M., and Ingraffea, A. R. (1981). “Mixed-mode crack propagation in mortar and concrete.”Dept. of Struct. Engrg. Rep. 81-13, Cornell Univ., Ithaca, N.Y.
2.
Bažant, Z. P.(1983). “Comment on orthotropic models for concrete and geomaterials.”J. Engrg. Mech., ASCE, 109, 849–865.
3.
Belytschko, T., Fish, J., and Engelmann, B. E.(1988). “A finite element with embedded localization zones.”Computer Methods in. Appl Mech. Engrg., 70, 59–89.
4.
Clough, R. W. (1962). “The stress distribution of Norfolk dam.”Inst. of Engrg. Res., Series 100, Issue 19, Univ. of California, Berkeley, Calif.
5.
Cope, R. J., Rao, P. V., Clark, L. A., and Norris, P. (1980). “Modelling of reinforced concrete behaviour for finite element analysis of bridge slabs.”Numerical methods for nonlinear problems 1, C. Taylor et al., eds., Pineridge Press, Swansea, Wales, U.K., 457–470.
6.
de Borst, R. (1986). “Non-linear analysis of frictional materials,” PhD thesis, Delft Univ. of Technol., Delft, The Netherlands.
7.
Droz, P. (1987). “Modèle numérique du comportement non-linéaire d'ouvrages massifs en béton non armé,” PhD thesis, Swiss Fed. Inst. of Technol. at Lausanne (EPFL), Switzerland.
8.
Dvorkin, E. N., Cuitiño, A. M., and Gioia, G.(1990). “Finite elements with displacement interpolated embedded localization lines.”Int. J. Numer. Methods in Engrg., 30, 541–564.
9.
“Finite element analysis of fracture in concrete structures.” (1997). ACI Rep. 446.3R, Am. Concrete Inst., Detroit, Mich.
10.
“Fracture mechanics of concrete: Concepts, models, and determination of material properties.” (1991). ACI Rep. 446.1R, Am. Concrete Inst., Detroit, Mich.; reprinted in Fracture mechanics of concrete structures (1991), Z. P. Bažant, ed., Elsevier, London, England and New York, N.Y., 1–140.
11.
Gupta, A. K., and Akbar, H.(1984). “Cracking in reinforced concrete analysis.”J. Engrg. Mech., ASCE, 110, 1735–1746.
12.
Jirásek, M., and Zimmermann, Th.(1998). “Rotating crack model with transition to scalar damage.”J. Engrg. Mech., ASCE, 124(3), 277–284.
13.
Klisinski, M., Runesson, K., and Sture, S.(1991). “Finite element with inner softening band.”J. Engrg. Mech., ASCE, 117, 575–587.
14.
Larsson, R., and Runesson, K.(1996). “Element-embedded localization band based on regularized displacement discontinuity.”J. Engrg. Mech., ASCE, 122, 402–411.
15.
Lotfi, H. R., and Shing, B. B.(1995). “Embedded representation of fracture in concrete with mixed finite elements.”Int. J. Numer. Methods in Engrg., 38, 1307–1325.
16.
Needleman, A., and Tvergaard, V. (1982). “Finite element analysis of localization in plasticity.”Finite elements—Special problems in solid mechanics, J. T. Oden and G. F. Carey, eds., Prentice-Hall, Englewood Cliffs, N.J.
17.
Ngo, D., and Scordelis, A. C.(1967). “Finite element analysis of reinforced concrete beams.”J. Am. Concrete Inst., 64, 152–163.
18.
Oliver, J.(1989). “A consistent characteristic length for smeared cracking models.”Int. J. Numer. Methods in Engrg., 28, 461–474.
19.
Ortiz, M., Leroy, Y., and Needleman, A.(1987). “A finite element method for localized failure analysis.”Computer Methods in Appl. Mech. Engrg., 61, 189–214.
20.
Pastor, M., and Quecedo, M.(1995). “A patch test for mesh alignment effects in localized failure.”Communications in Numerical Methods in Engrg., 11, 1015–1024.
21.
Rashid, Y. R.(1968). “Analysis of prestressed concrete pressure vessels.”Nuclear Engrg. and Design, 7, 334–344.
22.
Rots, J. G. (1988). “Computational modeling of concrete fracture,” PhD thesis, Delft Univ. of Technol., Delft, The Netherlands.
23.
Simo, J. C., Oliver, J., and Armero, F.(1993). “An analysis of strong discontinuities induced by strain softening in rate-independent inelastic solids.”Int. J. Comp. Mech., 12, 277–296.
24.
Steinmann, P., and Willam, K.(1991a). “Performance of enhanced finite element formulations in localized failure computations.”Computer Methods in Appl. Mech. Engrg., 90, 845–867.
25.
Steinmann, P., and Willam, K.(1991b). “Finite elements for capturing localized failure.”Arch. Appl. Mech., 61, 259–275.
26.
Tvergaard, V., Needleman, A., and Lo, K. K.(1981). “Flow localization in the plain strain tensile test.”Mech. Phys. Solids, 29, 115–142.
27.
Willam, K., Pramono, E., and Sture, S. (1987). “Fundamental issues of smeared crack models.”Fracture of concrete and rock, S. P. Shah and S. E. Swartz, eds., Soc. for Experimental Mech., Bethel, Conn., 192–207.
28.
Zimmermann, Th., and Li, Y.-J. (1993). “Numerical simulation of smeared crack propagation in geomaterials: An evaluation of the rotating crack model.”Proc., Applications of Comp. Methods in Rock Mech., Xian, PRC, 123–127.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 124Issue 8August 1998
Pages: 842 - 851

History

Published online: Aug 1, 1998
Published in print: Aug 1998

Permissions

Request permissions for this article.

Authors

Affiliations

Milan Jirásek
Res. Assoc., Dept. of Civ. Engrg., Swiss Fed. Inst. of Technol. (EPFL), 1015 Lausanne, Switzerland.
Thomas Zimmermann
Lect., Dept. of Civ. Engrg., Swiss Fed. Inst. of Technol. (EPFL), 1015 Lausanne, Switzerland.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share