Second-order bifurcation in elastic-plastic solidS |
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Authors: | H Petryk K Thermann |
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Institution: | Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland;Abteilung Maschinenbau, Universität Dortmund, 46 Dortmund 50, Federal Republic of Germany |
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Abstract: | Second-order rate constitutive equations are formulated for a time-independent elastic-plastic material, obeying the normality flow rule with a smooth yield surface. Under specified regularity restrictions imposed on the involved fields, the regular second-order rate boundary value problem with quasistatic accelerations as unknowns is posed. It is shown that every solution of this generally non-linear rate problem is governed by a variational principle and that the corresponding functional reaches a strict absolute minimum, provided the solution satisfies a sufficient uniqueness condition. With the same incrementally linear comparison solid, Hill's exclusion condition rules out not only a first- but also a second-order bifurcation. The criticality of the exclusion condition is discussed and conditions are indicated under which a second-order bifurcation becomes possible, while the first-order rate problem is still uniquely solvable. |
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