A finite element with embedded localization zones. (English) Zbl 0653.73032

A method is developed by which localization zones can be embedded in four-node quadrilaterals and related elements. This is accomplished by modifying the strain field within the framework of a three-field variational statement. The jumps in strain associated with the localization band are obtained by imposing traction continuity and compatibility within the element; the latter follows naturally from the variational statement. Several one- and two-dimensional applications are shown.


74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
74S30 Other numerical methods in solid mechanics (MSC2010)


Zbl 0592.73019
Full Text: DOI


[1] Hill, R., Bifurcation and uniqueness in nonlinear mechanics of continua, (), 155-164
[2] Rice, J.R., The localization of plastic deformation, (), 207-220
[3] Rudnicki, J.W.; Rice, J.R., Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. mech. phys. solids, 23, 371-394, (1975)
[4] Needleman, A., Material rate dependence and mesh sensitivity in localization problems, Comput. meths. appl. mech. engrg., 67, 69-87, (1987) · Zbl 0618.73054
[5] D. Lasry and T. Belytschko, Localization limiters in transient problems, Internat. J. Solids and Structures (to appear). · Zbl 0636.73021
[6] Tvergaard, V.; Needleman, A.; Lo, K.K., Flow localization in the plane strain tensile test, Mech. phys. solids, 29, 2, 115-142, (1981) · Zbl 0462.73082
[7] Needleman, A.; Tvergaard, V., Finite element analysis of localization in plasticity, (), 95-297
[8] Ortiz, M.; Leroy, Y.; Needleman, A., A finite element method for localized failure analysis, Comput. meths. appl. mech. engrg., 61, 189-214, (1987) · Zbl 0597.73105
[9] Wilson, E.L.; Taylor, R.L.; Doherty, W.P.; Ghaboussi, J., Incompatible displacement models, (), 45-58
[10] Bazant, Z.P.; Belytschko, T.; Chang, T.P., Continuum theory for strain softening, ASCE J. engrg. mech., 110, 1666-1692, (1984)
[11] Pietruszak, S.T.; Mroz, Z., Finite element analysis of deformation of strain softening materials, Internat. J. numer. meths. engrg., 17, 327-334, (1981) · Zbl 0461.73063
[12] Bazant, Z.P.; Cedolin, L., Blunt crack propagation in finite element analysis, ASCE J. engrg. mech., 105, 297-313, (1979)
[13] Simo, J.C.; Hughes, T.J.R., On the variational foundations of assumed strain methods, ASME J. appl. mech., 53, 51-54, (1986) · Zbl 0592.73019
[14] Hughes, T.J.R., Generalization of selective integration procedures to anisotropic and nonlinear media, Internat. J. numer. meths. engrg., 15, 1413-1418, (1980) · Zbl 0437.73053
[15] Belytschko, T.; Engelmann, B.E., On flexurally superconvergent four-node quadrilaterals, Comput. & structures, 25, 909-918, (1987) · Zbl 0607.73073
[16] Hill, R., Acceleration waves in solids, J. mech. phys. solids, 10, 1-16, (1962) · Zbl 0111.37701
[17] Belytschko, T.; Bachrach, W.E., Efficient implementation of quadrilaterals with high coarse-mesh accuracy, Comput. meths. appl. mech. engrg., 54, 279-301, (1986) · Zbl 0579.73075
[18] Bazant, Z.P.; Belytschko, T., Wave propagation in a strain-softening bar: exact solution, ASCE J. engrg. mech., 111, 381-389, (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.