Parameter-Estimation Algorithms for Characterizing a Class of Isotropic and Anisotropic Viscoplastic Material Models

Abstract

A number of robust, and computationally efficient, algorithms arepresented for the development of an overall strategy to estimate thematerial parameters characterizing a class of complex viscoplasticmaterial models (i.e., rate dependent plastic flow, nonlinear kinematichardening, thermal/static recovery, isotropic and anisotropic, etc.). Theentire procedure is automated through the integrated software COMPARE(an acronym for COnstitutive Material PARameter Estimator) to enable thedetermination of an `optimum' set of material parameters by minimizingthe errors between the experimental test data and the predictedresponse. The key ingredients of COMPARE are: (i) primal analysisutilizing the unconditionally-stable, fully implicit, integration schemefor the models' underlying flow and evolutionary rate equations; (ii) sensitivity analysis utilizing a direct-differentiation approach (i.e.,explicit, `exact' expressions are derived); (iii) a gradient-basedoptimization technique of an error/cost function; and (iv) graphicaluser interface. The estimation of the material parameters is cast as aminimum-error, weighted-multi-objective, nonlinear optimization problemwith constraints. Comparison between the sensitivities obtained by theproposed direct scheme and those produced by conventional finitedifference techniques is presented to assess accuracy. Detailedderivations are given, together with the results generated by applyingthe developed algorithms to a comprehensive set of test matrices. Theseinclude constant strain-rate tension, creep, and relaxation tests, forboth isotropic as well as anisotropic behaviors.