On the Bifurcation and Postbifurcation Theory for a General Class of Elastic-Plastic Solids
The present work is concerned with the bifurcation and postbifurcation analysis of a class of rate independent plasticity models obeying Hill’s maximum dissipation principle. A variational inequality approach, which differs from the classical formulation of the plastic bifurcation problem, is employed. The rate n bifurcation problem is formulated and sufficient conditions for uniqueness of the corresponding boundary value problem are given. A connection is made with Hill’s nonbifurcation criterion. In addition the issue of the postbifurcation behavior of the solid is addressed in this more general context showing the possiblity of angular as well as smooth bifurcations of rate n > 1.
Finally an example, capable of exhibiting both an angular as well as a smooth bifurcation is analyzed using the general formulation derived in this work. The presentation is concluded with some comments and comparisons of the present methodology with the classical approach.
KeywordsVariational Inequality Positive Definitness Bifurcation Problem Bifurcate Solution Plastic Solid
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- (1).CONSIDERE, A. Resistance des Pieces Comprimees. Congr. Intl. Proc. Const. (1891), p. 371, ParisGoogle Scholar
- (2).VON KARMAN, T. Untensuchungen Uder Knickfestigkeit, Mitteilungen Uder Forchungsarbeiten. Ver. Deut. Ing.,(1910), Vol. 81 Google Scholar
- (7).HUTCHINSON, J.W. Plastic Buckling. Advances Appl. Mech.,(1974), Vol. 14, p. 67 (8) KOTTER, W.T. On the stability of Elastic Equilibrium. Doctoral Thesis (1945), Delft.Google Scholar
- (11).NGUYEN, Q.S. Contribution a la Theorie Macroscopique de l’ Elastoplasticite avec Ecrouissage. Doctoral Thesis,(1973) ParisGoogle Scholar
- (15).NGUYEN,Q.S.and TRIANTAFYLLIDIS, N. Plastic Bifurcation and Post - Bifurcation Analysis for Generalized Standard Continua. J. Mech. Phys. Solids, (1989), Vol. 27, p. 465Google Scholar
- (16).NGUYEN, Q.S. and STOLZ, C. Sur la Methode du Developpement Asymptotique en Flambage Plastique.C.R. Acad. Sci. Paris, (1985), V. 300, Ser. II, No. 7, p. 235Google Scholar
- (17).NGUYEN, Q.S. Problemes de Plasticite et de Rupture, Course Notes,(1980), Univ. of Orsay.Google Scholar