Identification of material parameters for inelastic constitutive models: statistical analysis and design of experiments

In this paper we introduce stochastic methods to describe the influence of scattering test data on the identification of material parameters. We employ the viscoplastic constitutive model of Chan, Bodner, and Lindholm in its uniaxial form. The available test data result from three types of experiments performed at 600 °C on AINSI SS316 stainless steel, namely creep tests, constant strain rate tension tests with intermediate relaxation, and cyclic tension–compression tests. Each test has been performed with 12 specimens at different strain rates and stress rates respectively. However, for a serious statistical evaluation a larger number of experiments is required. In order to increase the number of tests we introduce stochastic simulations based on time series analysis which generate artificial data with the same stochastic behaviour as the experimental data. The method of stochastic simulation presents a widely accepted technique in engineering which does not add complexity to the process of parameter identification, but allows an investigation of the confidence in the fits of the material parameters. To keep the computation time for the identification of the material parameters as low as possible, very efficient numerical methods have to be implemented. The methods applied here for integration and nonlinear optimization are briefly introduced. The optimization strategy contains stochastic elements. Furthermore, we apply the method of statistical design of experiments to derive which combination of tests yields the most important information for an effective identification of material parameters.