Developing constitutive model parameters via a multi-scale approach

  • B. S. AnglinEmail author
  • B. T. Gockel
  • A. D. Rollett


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.


Optimization Constitutive law Pearlite Viscoplastic Multi-scale 



Use of the Garnet machine at the ERDC DSRC for completion of this work is gratefully acknowledged. The support of the High Performance Computing Modernization Office via the Productivity Enhancement, Technology Transfer and Training (PETTT) program is also acknowledged.


This research was supported in part (BSA) by an appointment to the Postgraduate Research Participation Program at the U.S. Army Research Laboratory administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and USARL. ADR acknowledges support from the National Science Foundation under DMR 1435544.


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Authors and Affiliations

  1. 1.Materials Response and Design BranchUS Army Research LaboratoryAberdeen Proving GroundUSA
  2. 2.U.S. Air Force Research LaboratoryWright-PattersonUSA
  3. 3.Department of Materials Science and EngineeringCarnegie Mellon UniversityPittsburghUSA

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