Paper Number
TM8 

Session
Rheometry: Advanced Techniques and Methods

Title
Medium amplitude parallel superposition (MAPS) rheology

Presentation Date and Time
October 21, 2019 (Monday) 2:20

Track / Room
Track 1 / Room 305A

Authors (Click on name to view author profile)

  1. Swan, James (MIT, Chemical Engineering)
  2. McKinley, Gareth H. (Massachusetts Institute of Technology, Department of Mechanical Engineering)
  3. Lennon, Kyle (MIT, Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
James Swan1, Gareth H. McKinley2, and Kyle Lennon1
1Chemical Engineering, MIT, Cambridge, MA 02139; 2Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA

Speaker / Presenter 
Swan, James

Text of Abstract
A mathematical representation for nonlinear viscoelasticity based on Volterra series expansion of the shear stress as a functional of the shear strain is presented. In this work, we develop a new theoretical and experimental framework based on this Volterra series representation, which we call medium amplitude parallel superposition (MAPS) rheology. The framework reveals a new material property, the third order complex modulus, that describes completely the weak, time-dependent nonlinearities of the shear stress within a homogeneously-sheared viscoelastic material. This nonlinear modulus is a unifying super-set of the response functions measured in medium amplitude oscillatory shear (MAOS) and parallel superposition (PS) experiments. Unlike the MAOS and PS transfer functions, the third order complex modulus can be used to construct the weakly nonlinear shear stress in response to an arbitrary shear history. This material function offers a new data-rich approach for completely characterizing the nonlinear viscoelasticity of unknown materials at third order in the magnitude of the deformation. For some simple constitutive models, the third order complex modulus possess startlingly complex and distinctive features. An experimental protocol is presented that allows for direct measurement of the third order complex modulus using existing commercial rheometers and their associated control software. We demonstrate this experimental protocol through measurement of the nonlinear viscoelastic response in a polymer hydrogel that possesses an ultra-narrow distribution of equilibrium relaxation times.