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

A number of robust, and computationally efficient, algorithms are presented for the development of an overall strategy to estimate the material parameters characterizing a class of complex viscoplastic material models (i.e., rate dependent plastic flow, nonlinear kinematic hardening, thermal/static recovery, isotropic and anisotropic, etc.). The entire procedure is automated through the integrated software COMPARE (an acronym for COnstitutive Material PARameter Estimator) to enable the determination of an ‘optimum’ set of material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are: (i) primal analysis utilizing the unconditionally-stable, fully implicit, integration scheme for 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-based optimization technique of an error/cost function; and (iv) graphical user interface. The estimation of the material parameters is cast as a minimum-error, weighted-multi-objective, nonlinear optimization problem with constraints. Comparison between the sensitivities obtained by the proposed direct scheme and those produced by conventional finite difference techniques is presented to assess accuracy. Detailed derivations are given, together with the results generated by applying the developed algorithms to a comprehensive set of test matrices. These include constant strain-rate tension, creep, and relaxation tests, for both isotropic as well as anisotropic behaviors.