On smooth bifurcations in non-associative elastoplasticity

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. Copyright (C) 1996 Elsevier Science Ltd