Paper Number
PO4 

Session
Poster Session

Title
Medium amplitude parallel superposition (MAPS) rheology

Presentation Date and Time
October 23, 2019 (Wednesday) 6:30

Track / Room
Poster Session / Ballroom C on 4th floor

Authors (Click on name to view author profile)

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

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

Speaker / Presenter 
Lennon, Kyle

Text of Abstract
A new mathematical representation for nonlinear viscoelasticity based on the Volterra series expansion of the nonlinear functional relationship between shear stress and strain history is presented. We develop the theoretical and experimental framework for this representation, which we call medium amplitude parallel superposition (MAPS) rheology, and reveal a new material property, called the third order complex modulus. This material property describes completely the weakly nonlinear response of a viscoelastic material to an arbitrary homogenous shear deformation history. We show that the third order complex modulus is a super-set of the properties measured in medium amplitude oscillatory shear (MAOS) and parallel superposition (PS) measurements. A straightforward method for visualizing the third order complex modulus in theoretical and experimental studies is then proposed, which exploits symmetries of the response function to reduce it to a minimal domain. The third order complex modulus is computed and plotted for a few phenomenological constitutive models to illustrate the richness of the MAPS framework. Finally, an experimental protocol is presented, which allows high-throughput direct measurements of the third order complex modulus using commercially available rheometers, and this protocol is applied to measurements of nonlinear viscoelasticity in a model material.