Finite‐Element Analysis of Elastoplastic Discontinuities
Publication: Journal of Engineering Mechanics
Volume 120, Issue 11
Abstract
In the present paper we address the question of whether localized failure due to elastoplastic bifurcation can be captured within the fixed‐mesh approach. To this end, the theoretical framework of localization analysis of elastoplastic solids is revisited, and examples of weak discontinuities are presented for an elastic perfectly plastic Huber‐Mises material with focus on plane stress. The prominent role of finite‐element design (standard displacement versus enriched formulation) and orientation (aligned versus misaligned geometry) is demonstrated first at the element level, when a single element is uniformly stretched to the yield limit and subjected to localization at all Gauss points. The weak localization test probes the directional properties of the finite element when spatial discontinuities in the strain field are to be captured. This element test is subsequently extended to the structural level and is illustrated with the eigenanalysis of a flat steel bar that is uniformly stretched to the yield limit in uniaxial tension. The effect of mesh alignment is examined with a layer of finite elements that is gradually rotated towards the spatial discontinuity of elastoplastic bifurcation analysis.
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References
1.
de Borst, R., and Mühlhaus, H.‐B. (1991). “Continuum models for discontinuous media.” Proc., RILEM Symp. on fracture processes in concrete, rock and ceramics, J. G. M. van Mier, J. G. Rots, and A. Bakker, eds., Chapman & Hall, London, 601–618.
2.
Dietsche, A., Steinmann, P., and Willam, K. (1993). “Micropolar elasto‐plasticity and its role in localization.” Int. J. Plast., 9(7), 813–831.
3.
Nadai, A. (1950). Theory of flow and fracture of solids, McGraw‐Hill, New York, N.Y.
4.
Needleman, A. (1988). “Material rate dependence and mesh sensitivity in localization problems.” Comp. Methods Appl. Mech. Engrg., 67, 69–85.
5.
Ortiz, M., and Quigley, J. J. (1991). “Adaptive mesh refinement in strain localization problems.” Comp. Methods Appl. Mech. Engrg., 90(1–3), 781–804.
6.
Rice, J. R. (1976). “The localization of plastic deformation.” Theoretical and applied mechanics, W. T. Koiter, ed., North Holland Publishing Co., Amsterdam, The Netherlands, 207–220.
7.
Simo, J. C., and Rifai, M. S. (1990). “A class of mixed assumed strain methods and the method of incompatible modes.” Int. J. Num. Meth. Engrg., 29(8), 1595–1638.
8.
Steinmann, P., and Willam, K. (1991). “Performance of enhanced finite element formulations in localized failure computations.” Comp. Methods Appl. Mech. Engrg., 90(1–3), 845–867.
9.
Steinmann, P., and Willam, K. (1992). “Adaptive techniques for localization analysis.” Adaptive, multilevel and hierarchical computational strategies, A. Noor, ed., ASME, New York, N.Y., 437–462.
10.
Vardoulakis, I., and Aifantis, E. C. (1991). “A gradient theory of plasticity for granular materials.” Acta Mechanica, 87(3–4), 197–217.
11.
Willam, K., Bicanic, N., Pramono, E., and Sture, S. (1986). “Composite fracture model for strain softening computations of concrete.” Proc., Symp. Fracture Toughness and Fracture Energy of Concrete, F. Wittmann, ed., Elsevier Science Publ., Amsterdam, The Netherlands, 149–162.
12.
Willam, K., and Dietsche, A. (1992). “Regularization of localized failure computations.” Proc., 3rd Int. Conf. Comp. Plasticity, COMPLAS III, E. Onate, E. Hinton, and R. Owen, eds., Pineridge Press, Swansea, U.K., 2185–2204.
13.
Wilson, E. L., Taylor, R. L., Doherty, W. P., and Ghaboussi, J. (1973). “Incompatible displacement models.” Proc., Numerical and Computer Models in Struct. Mech., S. J. Fenves et al., eds., Academic Press, New York, N.Y.
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Copyright © 1994 American Society of Civil Engineers.
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Received: Jun 15, 1993
Published online: Nov 1, 1994
Published in print: Nov 1994
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