Abstract
In this work, we revisit the seminal work of Renardy [M. Renardy, J. Non-Newtonian Fluid Mech. 52(1), 91–95 (1994)] on the reformulation of the stress tensor in its “natural” basis and present a generic framework for the natural-conformation tensor for a large class of differential constitutive models. We show that the proposed dyadic transformation can be equated as an orthogonal transformation of the conformation tensor into a streamlined orthonormal basis given by a rotation tensor expressed in terms of the unit velocity vectors. We also show that the natural-conformation tensor formulation is a particular sub-case of the kernel-conformation tensor transformation [A. M. Afonso, F. T. Pinho, M. A. Alves, J. Non-Newtonian Fluid Mech. 167–168, 30–37 (2012)] with the kernel function acting on the rotation of the eigenvectors rather than on the magnitude of the extension of the conformation tensor.
| Original language | English |
|---|---|
| Article number | 111706 |
| Journal | Physics of Fluids |
| Volume | 37 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 30 Nov 2025 |
Data Availability Statement
The data that support the findings of this study are available within the article.Funding
A. M. Afonso acknowledges FCT – Fundação para a Ciência e a Tecnologia for financial support through Nos. LA/P/0045/2020 (ALiCE), UIDB/00532/2020, UIDP/00532/2020 (CEFT), and UID/532/2025, funded by national funds through FCT/MCTES (PIDDAC). J. D. Evans would like to acknowledge support from FAPESP-SPRINT Grant No. 2018/22242-0 and thank the University of Bath for sabbatical leave in 2023-2024. I. L. Palhares Junior would like to acknowledge support from FAPESP – CEPID/CeMEAI Grant No. 2013/07375-0, FAPESP – SPRINT Grant No. 2024/01651-0, and FAPESP – ANR Grant No. 2024/04769-1
ASJC Scopus subject areas
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes