Stress singularities of some common kernel transformed viscoelastic models

Jonathan D. Evans; I.L. Palhares Junior; A.M. Afonso

doi:10.1016/j.jnnfm.2026.105583

Stress singularities of some common kernel transformed viscoelastic models

Jonathan D. Evans, I.L. Palhares Junior, A.M. Afonso

Research output: Contribution to journal › Article › peer-review

Abstract

The kernel conformation tensor is a powerful generic transformation for a large class of differential constitutive models. We derive its stress singularity associated with the stretching solution of the viscoelastic extra-stress tensor. This is relevant to re-entrant corner flows in contraction/expansion flows and the separation of a free-surface from a solid surface at the die lip in extrudate swell. The theoretical asymptotic results are compared to numerical scheme results for the two common kernel conformation cases of natural logarithm and square-root. These results are presented for the viscoelastic models in which the asymptotic stress-tensor singularity is currently known analytically, namely UCM/Oldroyd-B, sPTT and Giesekus.

Original language	English
Article number	105583
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	349
Early online date	18 Mar 2026
DOIs	https://doi.org/10.1016/j.jnnfm.2026.105583
Publication status	E-pub ahead of print - 18 Mar 2026

Data Availability Statement

No data was used for the research described in the article.

Funding

J.D. Evans acknowledges financial support from FAPESP-SPRINT grants 2018/22242-0 and 2024/01651-0 , and would like to thank the University of Bath for sabbatical leave during 2023–2024. A. M. Afonso acknowledges FCT - Fundação para a Ciência e a Tecnologia for financial support through LA/P/0045/2020 (ALiCE), UIDB/00532/2020 and UIDP/00532/2020 (CEFT), funded by national funds through FCT/MCTES (PIDDAC) . I.L. Palhares Junior would like to acknowledge support from CEPID-CeMEAI (FAPESP grant no. 2013/07375-0 ) and FAPESP-SPRINT grant no. 2024/01651-0 and FAPESP-ANR grant no. 2024/04769-1 . The authors also acknowledge the Numerical Simulation and AI Laboratory at FCT/UNESP for their support with cluster resources.

Funders	Funder number
FAPESP-SPRINT

Keywords

Kernel-conformation singularities
Non-Newtonian flows
Viscoelastic models

ASJC Scopus subject areas

General Chemical Engineering
General Materials Science
Condensed Matter Physics
Mechanical Engineering
Applied Mathematics

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10.1016/j.jnnfm.2026.105583Licence: CC BY

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title = "Stress singularities of some common kernel transformed viscoelastic models",

abstract = "The kernel conformation tensor is a powerful generic transformation for a large class of differential constitutive models. We derive its stress singularity associated with the stretching solution of the viscoelastic extra-stress tensor. This is relevant to re-entrant corner flows in contraction/expansion flows and the separation of a free-surface from a solid surface at the die lip in extrudate swell. The theoretical asymptotic results are compared to numerical scheme results for the two common kernel conformation cases of natural logarithm and square-root. These results are presented for the viscoelastic models in which the asymptotic stress-tensor singularity is currently known analytically, namely UCM/Oldroyd-B, sPTT and Giesekus.",

keywords = "Kernel-conformation singularities, Non-Newtonian flows, Viscoelastic models",

author = "Evans, \{Jonathan D.\} and Junior, \{I.L. Palhares\} and A.M. Afonso",

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AU - Evans, Jonathan D.

AU - Junior, I.L. Palhares

AU - Afonso, A.M.

PY - 2026/3/18

Y1 - 2026/3/18

N2 - The kernel conformation tensor is a powerful generic transformation for a large class of differential constitutive models. We derive its stress singularity associated with the stretching solution of the viscoelastic extra-stress tensor. This is relevant to re-entrant corner flows in contraction/expansion flows and the separation of a free-surface from a solid surface at the die lip in extrudate swell. The theoretical asymptotic results are compared to numerical scheme results for the two common kernel conformation cases of natural logarithm and square-root. These results are presented for the viscoelastic models in which the asymptotic stress-tensor singularity is currently known analytically, namely UCM/Oldroyd-B, sPTT and Giesekus.

AB - The kernel conformation tensor is a powerful generic transformation for a large class of differential constitutive models. We derive its stress singularity associated with the stretching solution of the viscoelastic extra-stress tensor. This is relevant to re-entrant corner flows in contraction/expansion flows and the separation of a free-surface from a solid surface at the die lip in extrudate swell. The theoretical asymptotic results are compared to numerical scheme results for the two common kernel conformation cases of natural logarithm and square-root. These results are presented for the viscoelastic models in which the asymptotic stress-tensor singularity is currently known analytically, namely UCM/Oldroyd-B, sPTT and Giesekus.

KW - Kernel-conformation singularities

KW - Non-Newtonian flows

KW - Viscoelastic models

UR - https://www.scopus.com/pages/publications/105033549900

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DO - 10.1016/j.jnnfm.2026.105583

M3 - Article

SN - 0377-0257

VL - 349

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

M1 - 105583

ER -

Stress singularities of some common kernel transformed viscoelastic models

Abstract

Data Availability Statement

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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