Identification of plastic constitutive Johnson–Cook model parameters by optimization-based inverse method

Abstract

Abstract Because the design of most products incorporates numerical analysis such as the finite element method, these days, accurate determination of dynamic material model parameters is significant. Usually, the dynamic constitutive model parameters such as those in the Johnson–Cook (JC) model are determined by fitting stress–strain curves obtained by split Hopkins pressure bar (SHPB) tests at various strain rates and temperatures. However, the determination of model parameters by fitting cannot consider potential three-dimensional heterogeneities of stress propagation because the stress and strain are calculated with the assumption of one-dimensional wave propagation. In this study, to accurately determine plastic constitutive model parameters considering all of the potential heterogeneities of stress propagation, an optimization-based inverse method was proposed. Multiple objectives were defined with multiple experimental data that were obtained by SHPB tests at different conditions. The error was defined using transmitted and reflected bar signals obtained in experiments and finite element analysis with candidate model parameters. JC model parameters were set as design variables and determined to minimize the error. To show the reliability of the proposed method, experimental data were generated numerically by FE analysis with known model parameters. The parameters determined by the proposed method were compared with the known exact values. Model coefficients were also determined by fitting the stress–strain relations to show the superiority of the proposed method. Though the fitting of stress–strain curves can also reasonably determine the model coefficients, it was shown that the model parameters could be determined accurately by the proposed optimization-based inverse method.