Paper Number
TM14 My Program
Session
Techniques and Methods: Rheometry, Tribometry, Spectroscopy and Microscopy
Title
Chebyshev polynomial approach for first normal stress difference interpretation in LAOS
Presentation Date and Time
October 22, 2025 (Wednesday) 1:50
Track / Room
Track 7 / Sweeney Ballroom D
Authors
- Hedegaard, Aaron T. (3M Company)
Author and Affiliation Lines
Aaron T. Hedegaard
3M Company, Saint Paul, MN 55144
Speaker / Presenter
Hedegaard, Aaron T.
Keywords
experimental methods; methods
Text of Abstract
First normal stress differences in shear rheology are useful for understanding processing phenomena like die swell and predicting axial loads during shearing of soft solids in a confined geometry, such as the sliding of two plates bonded with an adhesive. These stresses can become particularly acute in large-strain applications. When investigating the resulting shear and normal stresses in large strain oscillatory shear (LAOS) using an approach utilizing Chebyshev polynomials of the first kind, the shear stress response is described using the odd-ordered polynomial terms. However, when attempting to naively apply a similar approach to the resulting normal stresses via the even-ordered polynomial terms, the analysis fails to capture the in-phase component of the normal stresses, suggesting a fundamental limitation of the approach. This manuscript describes an alternative approach that continues to employ Chebyshev polynomials of the first kind to describe the out-of-phase (rate-dependent) response of the normal stresses but employs Chebyshev polynomials of the second kind for the in-phase (strain-dependent) response. This reproduces the results from a Fourier transform approach but retains the advantages of Chebyshev polynomials such as readiness for physical interpretation and a data-fitting procedure that is agnostic of the collected time data. The manuscript closes with worked examples for materials of interest.