Scaled corrector and branch-switching in necking problems

Abstract

A new branch-switching procedure for necking problems by finite element method is proposed. The scaled corrector method adopted in this paper for computing the critical eigenvector of the tangent stiffness matrix, which is indispensable to bifurcation analysis, is quite simple and effective for large scale problems because eigenvalue analysis is not required. The numerical background of the approximate critical eigenvector calculated during equilibrium iterations and the branch-switching procedure in elasto-plastic bifurcation problems are described in detail. As numerical examples, necking bifurcation problems of plane strain/stress states in finite strains are demonstrated to validate the proposed branch-switching procedure.