Development of Rheological Constitutive Modeling Method Using a Sparse Identification Algorithm: A Case Study for Extensional Flows

TL;DR

This study extends the Rheo-SINDy framework to extensional flows, successfully deriving constitutive models from numerical data and demonstrating its applicability beyond shear flow conditions.

Contribution

It applies Rheo-SINDy to extensional flow data, confirming its ability to identify known models and derive approximate constitutive models for complex rheological behaviors.

Findings

Rheo-SINDy accurately reproduces the Giesekus model under extensional flow.

It derives a simple approximate constitutive model for FENE dumbbell data.

The identified model reasonably predicts rheological properties, including extrapolation.

Abstract

Deriving constitutive models (CMs) from numerical data has been an attractive approach as a systematic CM building method. One recent study is Rheo-SINDy, which extended the sparse identification of nonlinear dynamics (SINDy) method to rheology. Although the Rheo-SINDy framework discovered an approximate CM from numerical data under shear flow, its versatility has not been investigated. To clarify its applicability to other types of flows, this study applied Rheo-SINDy to numerically generated data under extensional flow conditions. As baseline tests for extensional flow, we considered two problems: (i) whether the Rheo-SINDy framework can reproduce the famous Giesekus model from data generated by that model, and (ii) whether it can derive an approximate CM from data generated by a dumbbell model with a finite extensible nonlinear elastic (FENE) spring. For problem (i), we confirmed that Rheo-SINDy can identify the exact expression of the Giesekus model under extensional flow. For problem (ii), the Rheo-SINDy framework discovered a relatively simple expression of the approximate CM by manually designing the library matrix based on rheological knowledge. The identified approximate CM can reasonably predict extensional rheological properties of the FENE dumbbell model, including an extrapolation region. These findings demonstrate the fundamental validity of using Rheo-SINDy under extensional flow.