Abstract
The second-order incremental constitutive equations proposed by Petryk and Thermann [(1985) Second-order bifurcation in elastic-plastic solids. J. Mech. Phys. Solids 33, 577–593] are generalized to include non-associativity of the plastic flow rule. It is shown that the exclusion principle of Raniecki [(1979) Uniqueness criteria in solids with non-associated plastic flow laws at finite deformations. Bull. Acad. Polon. Ser. Sci. Tech. XXVII(8–9), 391–399] for first-order bifurcations is sufficient to exclude second-order bifurcations. The result holds true under specific regularity conditions and, accepting stronger regularity conditions, is extended to the case of nth-order bifurcations.
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