ON SMOOTH BIFURCATIONS IN NONASSOCIATIVE ELASTOPLASTICITY

The second-order incremental constitutive equations proposed by Petryk and Thermann [(1985) Second-order bifurcation in elastic-plastic soli ds. 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 tru e under specific regularity conditions and, accepting stronger regular ity conditions, is extended to the case of nth-order bifurcations. Cop yright (C) 1996 Elsevier Science Ltd