To solve problems in polymer fluid dynamics, one needs the equations of continuity, motion,
and energy. The last two equations contain the stress tensor and the heat-flux vector for the …

Viscoelasticity or rheology is important in polymer science and engineering because it plays
a crucial role in production and characterization of polymeric materials. Understanding the …

The Oldroyd 8-constant model is a continuum framework containing, as special cases, many
important constitutive equations for elastic liquids. When polymeric liquids undergo large …

The inverse Langevin function is an integral component for statistically-based network
models which describe rubber-like materials. This function is very important from theoretical …

In this paper, we provide a new exact framework for analyzing the most commonly measured
behaviors in large-amplitude oscillatory shear flow (LAOS), a popular flow for studying the …

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity
of popular special cases for polymeric liquids. In this paper, we use part of our exact solution …

The Oldroyd 8-constant continuum framework established a vision for constitutive equations
for polymeric liquids—past, present, and future. In this Letter, we bridge a macromolecular …

The method of harmonic balance (HB) is a spectrally accurate method used to obtain
periodic steady state solutions to dynamical systems subjected to periodic perturbations. We …

Recent work has focused on deepening our understanding of the molecular origins of the
higher harmonics that arise in the shear stress response of polymeric liquids in large …

This paper is motivated by Marchi and Arruda (Math Mech Solids, 2018), who developed
numerous approximations to the inverse Langevin function, minimizing their maximum …