Calibration of Elastoplastic Constitutive Model Parameters from Full-field Data with Automatic Differentiation-based Sensitivities

TL;DR

This paper introduces an automatic differentiation-based framework for calibrating elastoplastic model parameters using full-field data, enabling efficient gradient computation within a PDE-constrained optimization setting.

Contribution

It develops a novel AD-based method for elastoplastic model calibration that simplifies derivative calculations and enhances scalability and extensibility.

Findings

Verified correctness of the gradient calculations.

Demonstrated parallel computation on large-scale FE models.

Showcased ease of extending to other constitutive models.

Abstract

We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.