Localization Analysis of Nonlocal Model Based on Crack Interactions
Publication: Journal of Engineering Mechanics
Volume 120, Issue 7
Abstract
The conventional nonlocal model, often used as a localization limiter for continuum‐based constitutive laws with strain‐softening, has been based on an isotropic averaging function. It has recently been shown that this type of nonlocal averaging leads to a model that cannot satisfactorily reproduce experimental results for very different test geometries without modifying the value of the characteristic length depending on geometry. A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one‐dimensional description. Strain localization in an infinite layer under plane stress is studied using both the old and the new nonlocal formulations. The importance of a renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out. In addition to the detection of bifurcations from an initially uniform state, the stable branch of the load‐displacement diagram is followed using an incremental procedure.
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References
1.
Bažant, Z. P. (1984). “Imbricate continuum and its variational derivation.” J. Engrg. Mech., ASCE, 110(12), 1693–1712.
2.
Bažant, Z. P. (1988a). “Softening instability. Part I: localization into a planar band.” J. Appl. Mech., 55, 523–529.
3.
Bažant, Z. P. (1988b). “Stable states and paths of structures with plasticity or damage.” J. Engrg. Mech., ASCE, 114(12), 2013–2034.
4.
Bažant, Z. P. (1994a). “Errata.” J. Engrg. Mech., ASCE, 120(6), 1401–1402.
5.
Bažant, Z. P. (1994b). “Nonlocal damage theory based on micromechanics of crack interactions.” J. Engrg. Mech., ASCE, 120(3), 593–617.
6.
Bažant, Z. P., Belytschko, T. B., and Chang, T.‐P. (1984). “Continuum model for strain softening.” J. Engrg. Mech., ASCE, 110(12), 1666–1692.
7.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: elastic, inelastic, fracture and damage theories. Oxford University Press, New York, N.Y.
8.
Bažant, Z. P., and Lin, F.‐B. (1988). “Nonlocal yield‐limit degradation.” Int. J. Numerical Methods in Engrg., 26, 1805–1823.
9.
Bažant, Z. P., and Lin, F.‐B. (1989). “Stability against localization of softening into ellipsoids and bands: parameter study.” Int. J. Solids and Struct., 25, 1483–1498.
10.
Bažant, Z. P., and Oh, B.‐H. (1983). “Crack band theory for fracture of concrete.” Matériaux et Constructions, 16, 155–177.
11.
Bažant, Z. P., and Ožbolt, J. (1990). “Nonlocal microplane model for fracture, damage, and size effect in structures.” J. Engrg. Mech., ASCE, 116(11), 2485–2505.
12.
Bažant, Z. P., and Pijaudier‐Cabot, G. (1988). “Nonlocal continuum damage, localization instability and convergence.” J. Appl. Mech., 55, 287–293.
13.
Bažant, Z. P., and Prat, P. (1988a). “Microplane model for brittle plastic material. I: theory.” J. Engrg. Mech., ASCE, 114, 1672–1702.
14.
Bažant, Z. P., and Prat, P. (1988b). “Microplane model for brittle plastic material. II: verification.” J. Engrg. Mech., ASCE, 114, 1672–1702.
15.
Cosserat, E., and Cosserat, F. (1909). Théorie des corps déformables. Hermann, Paris, France (in French).
16.
de Borst, R., and Mühlhaus, H. B. (1991). “Continuum models for discontinuous media.” Symp. on Fracture Mech. of Brittle Disordered Mat., RILEM, Noordwijk, 19–21.
17.
de Borst, R., and Sluys, L. J. (1991). “Localization in a Cosserat continuum under static and dynamic loading conditions.” Computational Methods in Appl. Mech. and Engrg., 90, 805–827.
18.
Eringen, A. C. (1965). “Theory of micropolar continuum.” Proc., 9th Midwestern Mech. Conf., University of Wisconsin, Madison, Wisc., 23–40.
19.
Eringen, A. C. (1966). “A unified theory of thermomechanical materials.” Int. J. Engrg. Sci., 4, 179–202.
20.
Eringen, A. C., and Edelen, D. G. B. (1972). “On nonlocal elasticity.” Int. J. Engrg. and Sci., 10, 233–248.
21.
Kröner, E. (1967). “Elasticity theory of materials with long‐range cohesive forces.” Int. J. of Solids and Struct., 3, 731–742.
22.
Lasry, D., and Belytschko, T. (1988). “Localization limiters in transient problems.” Int. J. of Solids and Struct., 24, 581–597.
23.
Mühlhaus, H. B., and Vardoulakis, I. (1987). “The thickness of shear band in granular materials.” Géotechnique, London, England, 37, 271–283.
24.
Needleman, A. (1987). “Material rate dependence and mesh sensitivity in localization problems.” Computational Methods in Appl. Mech. and Engrg., 67, 68–85.
25.
Okui, Y., Horii, H., and Akiyama, A. (1993). “A continuum theory for solids containing microdeffects.” Int. J. of Engrg. Sci., 31(5), 735–749.
26.
Pietruszczak, S. T., and Mróz, Z. (1981). “Finite element analysis of deformation of strain‐softening materials.” Int. J. Numerical Methods in Engrg., 17, 327–334.
27.
Pijaudier‐Cabot, G., and Bažant, Z. P. (1987). “Nonlocal damage theory.” J. Engrg. Mech., ASCE, 113(10), 1512–1533.
28.
Schreyer, H., and Chen, Z. (1986). “One‐dimensional softening with localization.” J. Appl. Mech., 53, 791–797.
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Copyright © 1994 American Society of Civil Engineers.
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Received: Jul 28, 1993
Published online: Jul 1, 1994
Published in print: Jul 1994
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