The weakly nonlinear response and non-affine interpretation of the Johnson-Segalman/Gordon-Schowalter model

TL;DR

This paper derives analytical solutions for the Johnson-Segalman/Gordon-Schowalter model in medium-amplitude oscillatory shear, revealing time-strain separable nonlinearity and providing a new physical interpretation of non-affine deformation.

Contribution

It introduces new analytical solutions for the JS/GS model with a relaxation kernel, linking non-affine deformation to stress response and reinterpretation of previous MAOS data fitting.

Findings

Time-strain separable nonlinearity in JS/GS model

Unified framework including Maxwell models as subsets

Visualization of non-affine deformation field

Abstract

We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS (Martinetti & Ewoldt Phys. Fl. (2019)). The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.