A Substructuring Approach to Localized Plasticity Analysis

In the analysis of automotive structures using finite element models, areas of stress concentration are often uncovered. The calculated linear stress at these locations may exceed the yield strength of the material. In these situations, the analyst is confronted with the choice of making a nonlinear analysis of the structure or using an approximate technique to predict nonlinear strains. The former can be excessively expensive while the latter can lead to results of questionable accuracy. This paper will discuss a technique which substantially reduces the cost of the nonlinear analysis of complex structures with areas of localized plasticity.

The basis of the technique is the substructuring of the localized plasticity areas. They are identified and disconnected from the linear elastic part of the model by boundary points. The elastic degrees of freedom are reduced to boundary freedoms having boundary stiffness matrices which remain constant for each incremental step of a plasticity solution. The displacements for the last incremental step may be used to verify that the linearity of the elastic substructure has not been violated.

A brief description of the in-house computer programs are given. The technique, accuracy and savings are compared to a complete nonlinear analysis using two simple structures. Finally, the method is applied to a detailed automotive component.