Global optimization in material functions identification for voided media plastic flow

Abstract

The aim of this paper is to present an application of the global optimization method of Boender et al. to a material function identification in a mechanical problem. These material functions are found in the evolution equation for a volume void fraction parameter describing nucleation and growth of microvoids in the flow of porous ductile solids and they play an important role in proper constitutive modelling of postcritical behaviour and fracture. In the evolution equation a plastic strain controlled nucleation process is simulated and uniaxial tension deformation history is considered. In nonlinear regression the minimization of the mean squares functional is assumed. The problem is treated directly as a global optimization one. The necessity of the use of a global optimization approach follows from the hypothesis that there can exist many local minima in the considered problem. The possibility of the existence of many local minima is not usually taken into account. The global optimization method of Boender et al. was applied to minimize the least squares functional. We determine the material functions parameters on the basis of the given Fischer's [8] experimental data set. This data set has been obtained for axisymmetric tension of steel specimens. The results of numerical calculations presented in the paper proved the validity of the hypothesis about the existence of many local minima.