Numerical Calculation

Abstract

Elastoplastic deformation has to be analyzed generally by numerical calculations with finite incremental steps since the constitutive equation is rate nonlinear. In particular, the return-mapping algorithm to pull back the stress to the yield surface must be incorporated into the computer program adopting the conventional elastoplastic constitutive models. On the other hand, the subloading surface model is furnished with the distinguished advantage for the numerical calculation with the automatic controlling function to attract the stress to the normal-yield surface in the plastic deformation process and thus it does not require to incorporate the convergence computer algorithm such as the return mapping in the normal-yield state. Nevertheless, it requires to incorporate the return-mapping algorithm in the subyield state since the subyield state is out of the stress-controlling function. Basic equations for the return mapping method extended to the subloading surface model is described in this chapter.