Adaptive load incrementation algorithm during a process of local unloading in the elastic-plastic finite element analysis.

Abstract

There are two approaches in the incremental finite element analysis of elastic-plastic problems; one takes an explicit scheme using forward Euler integration formula with adaptive load incrementation, the so-called rmin method, and another implicit scheme with iterative procedures such as the Newton method. This paper discusses an algorithm of determining incremental step size in the former approach. A new additional restriction is proposed for the determination of the loading factor rmin when unloading takes place. A concept of admissible error is introduced where errors in stress increments are defined as the difference between one computed by assuming the elastic-plastic constitutive relation and the other computed by assuming the elastic relation. The error norm should be restricted within specified value. Numerical examples are demonstrated to show that the algorithm is reasonable.