Properties of Incremental Solutions for Dissipative Material
Publication: Journal of Engineering Mechanics
Volume 119, Issue 4
Abstract
Using the fully implicit rule for temporal integration, one may define a class of simple plasticity models, for which an incremental potential energy can be constructed. This potential has, in general, multiple stationary points, which correspond to equilibrium solutions when the material shows softening characteristics. Explicit expressions of the incremental potential energy are derived for von Mises plasticity with linear isotropic hardening within the context of a standard dissipative material. Using the Hill criterion for static stability, we show that stable incremental solutions are also (local) minimum points of the incremental potential energy for this particular material. Finite element results for this (simple) plasticity model are presented, which show that the stable solution also exhibits strong localization of plastic deformation.
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References
1.
Bazant, Z. P. (1988). “Stable states and paths of structures with plasticity or damage.” J. Engrg. Mech., ASCE, 114, 2013–2034.
2.
Bazant, Z. P. (1989). “Bifurcations and thermodynamic criteria of stable paths of structures exhibiting plasticity and damage propagation.” Computational plasticity; COMPLAS II, D. R. J. Owen, E. Hinton, and E. Onate, eds., Pineridge Press, 1–25.
3.
de Borst, R. (1987). “Computation of post‐bifurcation and post‐failure behavior of strain‐softening solids.” Comp. & Struct., 25, 211–224.
4.
de Borst, R., and Feenstra, P. H. (1990). “Studies in anisotropic plasticity with reference to the Hill criterion.” Int. J. Num. Meth. Engrg., 29, 315–336.
5.
Drucker, D. C. (1951). “A more fundamental approach to plastic stress‐strain relations.” Proc., 1st U.S. Nat. Congr. of Appl. Mech., Chicago, Ill., 487–491.
6.
Halphen, B., and Nguyen, Q. S. (1975). “Sur les materiaux standard géneralisés.” J. Mécanique, 14, 39–63 (in French).
7.
Hill, R. (1958). “A general theory of uniqueness and stability in elastic‐plastic solids.” J. Mech. Phys. Solids, 6, 236–249.
8.
Johnson, C. (1977). “A mixed finite element method for plasticity problems with hardening.” SIAM, J. Numer Anal., 14, 575–583.
9.
Klisinski, M., Mroz, Z., and Runesson, K. (1992). “Structure of constitutive equations in plasticity for different choices of state and control variables.” Int. J. Plasticity, 8, 221–243.
10.
Larsson, R., Runesson, K., and Sture, S. (1991). “Finite element simulation of localized plastic deformation.” Archive Appl. Mech., 61, 305–317.
11.
Larsson, R. (1990). “Numerical simulation of plastic localization,” Ph.D. thesis, Chalmers Univ. of Technol., S‐41296 Göteborg, Sweden.
12.
Larsson, R., Runesson, K., and Ottosen, N. S. (1992). “Discontinuous displacement approximation for capturing plastic localization.” Int. J. Num. Meth. Engrg.
13.
Martin, J. B. (1975). “A note on the implications of thermodynamic stability in the internal variable theory of inelastic solids.” Int. J. Solids Struct., 11, 247–253.
14.
Runesson, K., and Booker, J. R. (1982). “On mixed and displacement finite element methods in perfect elasto‐plasticity.” 4th Int. Conf. in Australia in Finite Element Methods, P. Hoadley and R. Stevens, eds., Melbourne, 85–89.
15.
Runesson, K., Samuelsson, A., and Bernspång, L. (1986). “Numerical technique in plasticity including solution advancement control.” Int. J. Num. Meth. Engrg., 22, 769–788.
16.
Runesson, K., Larsson, R., and Sture, S. (1989). “Characteristics and computational procedure in softening plasticity.” J. Engrg. Mech., ASCE, 115, 1628–1646.
17.
Runesson, K., and Mroz, Z. (1989). “A note on nonassociated plastic flow rules.” Int. J. Plasticity, 5, 639–658.
18.
Simo, J. C., and Taylor, R. L. (1985). “Consistent material operators for rate‐independent elasto‐plasticity.” Comp. Meth. in Appl. Mech. and Engrg., 48, 101–118.
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Published In
Journal of Engineering Mechanics
Volume 119 • Issue 4 • April 1993
Pages: 647 - 666
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Oct 15, 1992
Published online: Apr 1, 1993
Published in print: Apr 1993
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