Learning viscoplastic constitutive behavior from experiments: II. Dynamic indentation

TL;DR

This paper extends a method for identifying complex material behavior from experiments to include dynamic indentation with contact constraints, demonstrating its effectiveness on synthetic and real data.

Contribution

It introduces a novel approach to infer viscoplastic constitutive behavior under dynamic indentation, incorporating contact constraints and sensitivity analysis.

Findings

Successfully applied the method to synthetic data.

Validated the approach on experimental data from steel and aluminum alloys.

Extended the inverse problem framework to handle contact constraints.

Abstract

We continue the development of a method to accurately and efficiently identify the constitutive behavior of complex materials through full-field observations that we started in Akerson, Rajan and Bhattacharya (2024). 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 the model using the adjoint method. In this paper, we extend the approach to include contact and study dynamic indentation. Contact is a nonholonomic constraint, and we introduce a Lagrange multiplier and a slack variable to address it. We demonstrate the method on synthetic data before applying it to experimental observations on rolled homogeneous armor steel and a polycrystalline aluminum alloy.