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A Direct-adjoint Approach for Material Point Model Calibration with Application to Plasticity

Ryan Yan, D. Thomas Seidl, Reese E. Jones, Panayiotis Papadopoulos

TL;DR

This paper addresses calibrating local elastoplastic parameters by casting parameter identification as a constrained optimization problem driven by a material-point forward model. It introduces a direct-adjoint Hessian approach, computed with automatic differentiation, to enable true second-order optimization in Newton-type methods. The Hessian accuracy is validated against finite differences and complex-step checks, and two numerical tests show Newton-Raphson converges faster than gradient-based methods, even with noisy data and experimental tension data. The framework lays the groundwork for extending to full finite-element calibrated problems and offers a robust path to efficient parameter identification in plasticity models.

Abstract

This paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton-Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

A Direct-adjoint Approach for Material Point Model Calibration with Application to Plasticity

TL;DR

This paper addresses calibrating local elastoplastic parameters by casting parameter identification as a constrained optimization problem driven by a material-point forward model. It introduces a direct-adjoint Hessian approach, computed with automatic differentiation, to enable true second-order optimization in Newton-type methods. The Hessian accuracy is validated against finite differences and complex-step checks, and two numerical tests show Newton-Raphson converges faster than gradient-based methods, even with noisy data and experimental tension data. The framework lays the groundwork for extending to full finite-element calibrated problems and offers a robust path to efficient parameter identification in plasticity models.

Abstract

This paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton-Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.
Paper Structure (16 sections, 46 equations, 9 figures, 4 tables)

This paper contains 16 sections, 46 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Material Point Plasticity Forward Model
  3. Constitutive equations
  4. Model structure
  5. Inverse Problem Formulation
  6. Constrained optimization formulation
  7. Direct method
  8. Adjoint method
  9. Direct-adjoint method
  10. Parameter scaling
  11. Numerical Results
  12. A plane-stress problem
  13. Calibration with experimental tension data
  14. Conclusions
  15. Plane stress
  16. ...and 1 more sections

Figures (9)

  • Figure 1: Gradient comparisons to finite difference gradients
  • Figure 2: Direct-adjoint Hessian comparisons to finite difference Hessian
  • Figure 3: Comparison of calibrated model with synthetic data for $\sigma_{noise} = 5$ MPa
  • Figure 4: Comparison of calibrated model with synthetic data for $\sigma_{noise} = 10$ MPa
  • Figure 5: Convergence of plane-stress optimization problem for $\sigma_{noise} = 5$ MPa
  • ...and 4 more figures