Scaled corrector and branch-switching in necking problems

A new branch-switching procedure for necking problems by finite element met hod is proposed. The scaled corrector method adopted in this paper for comp uting the critical eigenvector of the tangent stiffness matrix, which is in dispensable to bifurcation analysis, is quite simple and effective for larg e scale problems because eigenvalue analysis is not required. The numerical background of the approximate critical eigenvector calculated during equil ibrium iterations and the branch-switching procedure in elasto-plastic bifu rcation problems are described in detail. As numerical examples, necking bi furcation problems of plane strain/stress states in finite strains are demo nstrated to validate the proposed branch switching procedure.