Learning constitutive relations from experiments: 1. PDE constrained optimization

TL;DR

This paper introduces a PDE-constrained optimization approach to identify complex constitutive relations of materials from experimental data, using adjoint methods for sensitivity analysis, demonstrated on synthetic quasistatic and dynamic problems.

Contribution

It presents a novel PDE-constrained inverse problem formulation for constitutive law identification, applicable to complex material models and demonstrated with synthetic data.

Findings

Method accurately recovers constitutive relations from synthetic data

Robust approach applicable to both quasistatic and dynamic problems

Flexible framework extendable to various material models

Abstract

We propose a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations. We formulate the problem of inferring constitutive relations from experiments as an indirect inverse problem that is constrained by the balance laws. Specifically, we seek to find a constitutive behavior that minimizes the difference between the experimental observation and the corresponding quantities computed with the model, while enforcing the balance laws. We formulate the forward problem as a boundary value problem corresponding to the experiment, and compute the sensitivity of the objective with respect to model using the adjoint method. The resulting method is robust and can be applied to constitutive models with arbitrary complexity. We focus on elasto-viscoplasticity, but the approach can be extended to other settings. In this part one, we formulate the method and demonstrate it using synthetic data on two problems, one quasistatic and the other dynamic.