Convergence of the Newton‐Raphson algorithm in elastic‐plastic incremental analysis
S. Caddemi, John B. Martin · International Journal for Numerical Methods in Engineering · 1991
Abstract A spatially continuous, time discrete formulation of the loading of an elastic, perfectly plastic body governed by a von Mises yield condition is presented. It is assumed that incremental changes in strain occur along minimum work paths, which is equivalent to a backward difference implicit integration algorithm or the radial return method. This assumption permits the incremental problem to be formulated as a convex non‐linear programming problem. The classical Newton‐Raphson algorithm can be adopted to provide an iterative solution of the non‐linear programming problem. It is shown that if an elastic or secant predictor modulus is used, the algorithm converges monotonically. However, if a tangent predictor is used, a line search algorithm must be included to ensure convergence.