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

TL;DR

This paper introduces a direct-adjoint method utilizing automatic differentiation for efficient calibration of elastoplastic material models, significantly improving optimization accuracy and convergence speed.

Contribution

It presents a novel direct-adjoint approach with automatic differentiation for Hessian computation, enhancing second-order optimization in material parameter calibration.

Findings

Newton-Raphson outperforms gradient-based methods

Hessian validation confirms accuracy

Calibration efficiency is improved

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.