Developing constitutive model parameters via a multi-scale approach

Abstract

Computing the mechanical response of materials requires accurate constitutive descriptions, especially their plastic behavior. Furthermore, the ability of a model to be used as a predictive, rather than a descriptive, tool motivates the development of physically based constitutive models. This work investigates combining a homogenized viscoplastic self-consistent (VPSC) approach to reduce the development time for a high-resolution viscoplastic model based on the fast Fourier transform (FFT). An optimization scheme based on a least-squares algorithm is presented. The constitutive responses of copper, interstitial-free steel, and pearlite are investigated, and the model parameters are presented. Optimized parameters from the low-fidelity model provide close agreement (<2 MPa, ~1 % error) with stress-strain data at low strains (<10 %) in the high-fidelity FFT model. Simple adjustments to constitutive law parameters bring the FFT stress-strain curve in alignment with experimental data at strains greater than 10 %. A two-phase constitutive law is developed for a pearlitic steel using a single stress-strain curve, supplemented by data for the constituent phases. Sources of error and methods of using material information are discussed that lead to optimal estimates of initial parameter values.