Parameter Estimation for an Internal Variable Model Using Nonlinear Optimization and Analytical/Numerical Response Sensitivities

Abstract

This paper demonstrates through examples that erroneous material constants for complex visco-plastic material models can be obtained from simultaneous parameter estimation by nonlinear optimization methods unless the laboratory load paths used in the fitting process give significant model response sensitivities to changes in all of the material parameters. A general procedure is proposed in which a nonlinear optimization algorithm is coupled with analytically/numerically derived response sensitivities to evaluate an unambiguous set of material parameters. Response sensitivities enter into the parameter estimation procedure in two ways. Relative response sensitivities are first used to identify an efficient test matrix that, when simulated with the model, give model responses that are sensitive to changes in each of the material parameters. Then the corresponding nonzero response sensitivities are used to construct the gradient and Hessian matrices in a gradient-driven optimization algorithm to evaluate the material parameters. A model for braze alloys is used to demonstrate that erroneous parameter values may result if not all of the relative response sensitivities are “nonzero” and distinct.