Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Time-strain separability in medium-amplitude oscillatory shear

Abstract

Here, we derive and study equations for the weakly nonlinear medium-amplitude oscillatory shear (MAOS) response of materials exhibiting time-strain separability. Results apply to constitutive models with arbitrary linear memory function $$\textit{m}$$(s) and for both viscoelastic liquids and viscoelastic solids. The derived equations serve as a reference to identify which models are time-strain separable (TSS) and which may appear separable but are not, in the weakly nonlinear limit. More importantly, we study how the linear viscoelastic (LVE) relaxation spectrum, H($$_\tau$$), affects the frequency dependence of the TSS MAOS material functions. Continuous relaxation spectra are considered that are associated with analytical functions (log-normal and asymmetric Lorentzian distributions), fractional mechanical models (Maxwell and Zener), and molecular theories (Rouse and Doi-Edwards). TSS MAOS signatures reveal much more than just the perturbation parameter A in the shear damping function small-strain expansion, $$h(_γ) = 1 + \text{A}_γ$$$$^2 + \mathcal{O}(_γ$$$$^4)$. Specifically, the distribution of terminal relaxation times is significantly more apparent in the TSS MAOS functions than their LVE counterparts. We theoretically show that this occurs because TSS MAOS material functions are sensitive to higher-order moments of the relaxation spectrum, which leads to the definition of MAOS liquids. We also show the first examples of MAOS signatures that differ from the liquid-like terminal MAOS behavior predicted by the fourth-order fluid expansion. This occurs when higher moments of the relaxation spectrum are not finite. The famous corotational Maxwell model is a subset of our results here, for which A = -1/6, and any LVE relaxation spectrum could be used.

Authors:
ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1607424
Grant/Contract Number:  
FG02-07ER46471
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 31; Journal Issue: 2; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 36 MATERIALS SCIENCE; Mechanical stress; Relaxation time spectrum; Zener model; Polymers; Materials analysis; Viscoelasticity; Constitutive relations; Maxwell models; Series expansion; Oscillatory shear measurements

Citation Formats

Martinetti, Luca, and Ewoldt, Randy H. Time-strain separability in medium-amplitude oscillatory shear. United States: N. p., 2019. Web. doi:10.1063/1.5085025.
Copy to clipboard
Martinetti, Luca, & Ewoldt, Randy H. Time-strain separability in medium-amplitude oscillatory shear. United States. https://doi.org/10.1063/1.5085025
Copy to clipboard
Martinetti, Luca, and Ewoldt, Randy H. Tue . "Time-strain separability in medium-amplitude oscillatory shear". United States. https://doi.org/10.1063/1.5085025. https://www.osti.gov/servlets/purl/1607424.
Copy to clipboard
@article{osti_1607424,
title = {Time-strain separability in medium-amplitude oscillatory shear},
author = {Martinetti, Luca and Ewoldt, Randy H.},
abstractNote = {Here, we derive and study equations for the weakly nonlinear medium-amplitude oscillatory shear (MAOS) response of materials exhibiting time-strain separability. Results apply to constitutive models with arbitrary linear memory function $\textit{m}$(s) and for both viscoelastic liquids and viscoelastic solids. The derived equations serve as a reference to identify which models are time-strain separable (TSS) and which may appear separable but are not, in the weakly nonlinear limit. More importantly, we study how the linear viscoelastic (LVE) relaxation spectrum, H($_\tau$), affects the frequency dependence of the TSS MAOS material functions. Continuous relaxation spectra are considered that are associated with analytical functions (log-normal and asymmetric Lorentzian distributions), fractional mechanical models (Maxwell and Zener), and molecular theories (Rouse and Doi-Edwards). TSS MAOS signatures reveal much more than just the perturbation parameter A in the shear damping function small-strain expansion, $h(_γ) = 1 + \text{A}_γ$$^2 + \mathcal{O}(_γ$$^4)$. Specifically, the distribution of terminal relaxation times is significantly more apparent in the TSS MAOS functions than their LVE counterparts. We theoretically show that this occurs because TSS MAOS material functions are sensitive to higher-order moments of the relaxation spectrum, which leads to the definition of MAOS liquids. We also show the first examples of MAOS signatures that differ from the liquid-like terminal MAOS behavior predicted by the fourth-order fluid expansion. This occurs when higher moments of the relaxation spectrum are not finite. The famous corotational Maxwell model is a subset of our results here, for which A = -1/6, and any LVE relaxation spectrum could be used.},
doi = {10.1063/1.5085025},
journal = {Physics of Fluids},
number = 2,
volume = 31,
place = {United States},
year = {Tue Jan 29 00:00:00 EST 2019},
month = {Tue Jan 29 00:00:00 EST 2019}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5085025
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Stopping of crosslinking reaction in a PDMS polymer at the gel point
journal, January 1985

  • Chambon, Francois; Winter, H. Henning
  • Polymer Bulletin, Vol. 13, Issue 6
  • DOI: 10.1007/bf00263470

Concentration and molecular weight dependence of viscoelastic properties in linear and star polymers
journal, November 1981

  • Raju, V. R.; Menezes, E. V.; Marin, G.
  • Macromolecules, Vol. 14, Issue 6
  • DOI: 10.1021/ma50007a011

Time and Temperature Dependence of the Ultimate Properties of an SBR Rubber at Constant Elongations
journal, November 1960

  • Smith, Thor L.; Stedry, Paul J.
  • Journal of Applied Physics, Vol. 31, Issue 11
  • DOI: 10.1063/1.1735470

Die Elastizität von Flüssigkeiten
journal, March 1966

The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release
journal, November 2001

  • Wagner, M. H.; Rubio, P.; Bastian, H.
  • Journal of Rheology, Vol. 45, Issue 6
  • DOI: 10.1122/1.1413503

Determination of relaxation time spectra by analytical inversion using a linear viscoelastic model with fractional derivatives
journal, November 1995

  • Friedrich, Chr.; Braun, H.; Weese, J.
  • Polymer Engineering and Science, Vol. 35, Issue 21
  • DOI: 10.1002/pen.760352102

Rheology of ordered and disordered symmetric poly(ethylenepropylene)-poly(ethylethylene) diblock copolymers
journal, April 1990

Significance of the Longest Rouse Relaxation Time in the Stress Relaxation Process at Large Deformation of Entangled Polymer Solutions
journal, June 2002

  • Inoue, Tadashi; Uematsu, Takehiko; Yamashita, Yasuhiro
  • Macromolecules, Vol. 35, Issue 12
  • DOI: 10.1021/ma012149g

Melt rheology of H-shaped polystyrenes
journal, November 1984

Effect of finite extensibility on the viscoelastic properties of a styrene–butadiene rubber vulcanizate in simple tensile deformations up to rupture
journal, April 1969

  • Smith, Thor L.; Dickie, Ray A.
  • Journal of Polymer Science Part A-2: Polymer Physics, Vol. 7, Issue 4
  • DOI: 10.1002/pol.1969.160070404

Elastoviscous Properties of Polyisobutylene. VI. Relation between Stress Relaxation Modulus and Dynamic Modulus
journal, August 1952

  • Tobolsky, Arthur V.
  • Journal of the American Chemical Society, Vol. 74, Issue 15
  • DOI: 10.1021/ja01135a021

Nonlinear viscoelastic characterization of a linear polyethylene (HDPE) melt in rotational and irrotational flows
journal, November 1998

Fractional relaxation in anelastic solids
journal, September 1994

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations
journal, January 2013

  • Jaishankar, Aditya; McKinley, Gareth H.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 469, Issue 2149
  • DOI: 10.1098/rspa.2012.0284

Time and Temperature Dependence of the Ultimate Properties of an SBR Rubber at Constant Elongations
journal, July 1961

  • Smith, Thor L.; Stedry, Paul J.
  • Rubber Chemistry and Technology, Vol. 34, Issue 3
  • DOI: 10.5254/1.3540259

The occurrence of self-similar relaxation in polymers
journal, September 1994

Continuous relaxation spectra for constitutive models in medium-amplitude oscillatory shear
journal, September 2018

  • Martinetti, Luca; Soulages, Johannes M.; Ewoldt, Randy H.
  • Journal of Rheology, Vol. 62, Issue 5
  • DOI: 10.1122/1.5025080

Rheology of Suspensions in Polymeric Liquids
journal, December 1985

Finite amplitude oscillations of viscoelastic fluids
journal, July 1991

  • Vrentas, J. S.; Venerus, D. C.; Vrentas, C. M.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 40, Issue 1
  • DOI: 10.1016/0377-0257(91)87023-q

Relaxation behavior of linear polymer chains with statistically distributed functional groups
journal, March 1989

  • Stadler, Reimund; De Lucca Freitas, Liane
  • Macromolecules, Vol. 22, Issue 2
  • DOI: 10.1021/ma00192a035

Scaling relations in nonlinear viscoelastic behavior of aqueous PEO solutions under large amplitude oscillatory shear flow
journal, January 2010

  • Cho, Kwang Soo; Song, Ki-Won; Chang, Gap-Shik
  • Journal of Rheology, Vol. 54, Issue 1
  • DOI: 10.1122/1.3258278

Relaxation and retardation functions of the Maxwell model with fractional derivatives
journal, March 1991

A constitutive analysis of uniaxial elongational flow data of low-density polyethylene melt
journal, January 1978

Similarities between Gelation and Long Chain Branching Viscoelastic Behavior
journal, May 2001

  • García-Franco, César A.; Srinivas, Srivatsan; Lohse, David J.
  • Macromolecules, Vol. 34, Issue 10
  • DOI: 10.1021/ma0021794

Frequency-sweep medium-amplitude oscillatory shear (MAOS)
journal, January 2018

  • Singh, Piyush K.; Soulages, Johannes M.; Ewoldt, Randy H.
  • Journal of Rheology, Vol. 62, Issue 1
  • DOI: 10.1122/1.4999795

Linear viscoelasticity of side chain liquid crystal polymer
journal, February 1993

Comparison of Simple Constitutive Equations for Polymer Melts in Shear and Biaxial and Uniaxial Extensions
journal, April 1987

  • Khan, S. A.; Larson, R. G.
  • Journal of Rheology, Vol. 31, Issue 3
  • DOI: 10.1122/1.549922

Power-law-like stress relaxation of block copolymers: disentanglement regimes
journal, March 1993

  • Rubinstein, Michael; Obukhov, S. P.
  • Macromolecules, Vol. 26, Issue 7
  • DOI: 10.1021/ma00059a038

A model for the viscoelastic behavior of rubberlike polymers including entanglement effects
journal, October 1962

  • Marvin, R. S.; Oser, H.
  • Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, Vol. 66B, Issue 4
  • DOI: 10.6028/jres.066b.019

Stressing behaviour in simple shear flow as predicted by a new constitutive model for polymer fluids
journal, January 1983

The Phenomenological Theory of Linear Viscoelastic Behavior
book, January 1989

A Study of Stress Relaxation with Finite Strain
journal, March 1963

  • Bernstein, B.; Kearsley, E. A.; Zapas, L. J.
  • Transactions of the Society of Rheology, Vol. 7, Issue 1
  • DOI: 10.1122/1.548963

Non-Markovian Configurational Diffusion and Reaction Coordinates for Protein Folding
journal, June 1998

Definitions of entanglement spacing and time constants in the tube model
journal, May 2003

  • Larson, R. G.; Sridhar, T.; Leal, L. G.
  • Journal of Rheology, Vol. 47, Issue 3
  • DOI: 10.1122/1.1567750

The Non-Linear Field Theories of Mechanics
book, January 2004

Recent Results in the Continuum Theory of Viscoelastic Fluids
journal, January 1961

A constitutive equation derived from the model of doi and edwards for concentrated polymer solutions and polymer melts
journal, October 1980

Dynamics of Entangled H-Polymers:  Theory, Rheology, and Neutron-Scattering
journal, October 1999

  • McLeish, T. C. B.; Allgaier, J.; Bick, D. K.
  • Macromolecules, Vol. 32, Issue 20
  • DOI: 10.1021/ma990323j

Anisotropic Fluid Theory: A Different Approach to the Dumbbell Theory of Dilute Polymer Solutions
journal, March 1972

  • Gordon, R. J.; Schowalter, W. R.
  • Transactions of the Society of Rheology, Vol. 16, Issue 1
  • DOI: 10.1122/1.549256

Rheology of concentrated microgel solutions
journal, September 1988

  • Ketz, R. J.; Prud'homme, R. K.; Graessley, W. W.
  • Rheologica Acta, Vol. 27, Issue 5
  • DOI: 10.1007/bf01329353

Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts
journal, November 2007

  • Hyun, Kyu; Baik, En Su; Ahn, Kyung Hyun
  • Journal of Rheology, Vol. 51, Issue 6
  • DOI: 10.1122/1.2790072

On the limit of linear viscoelastic response in the flow between eccentric rotating disks
journal, August 1978

  • Jongschaap, R. J. J.; Knapper, K. H.; Lopulissa, J. S.
  • Polymer Engineering and Science, Vol. 18, Issue 10
  • DOI: 10.1002/pen.760181009

IV. On the dynamical theory of gases
journal, January 1867

  • Maxwell, James Clerk
  • Philosophical Transactions of the Royal Society of London, Vol. 157, p. 49-88
  • DOI: 10.1098/rstl.1867.0004

Structure and viscoelasticity of matched asymmetric diblock and triblock copolymers in the cylinder and sphere microstructures
journal, December 1997

Measures of deformation and convected derivatives
journal, January 1979

Quantitative rheological model selection: Good fits versus credible models using Bayesian inference
journal, May 2015

  • Freund, Jonathan B.; Ewoldt, Randy H.
  • Journal of Rheology, Vol. 59, Issue 3
  • DOI: 10.1122/1.4915299

Step Shear Dynamics of Entangled Polymer Liquids
journal, June 2002

  • Sanchez-Reyes, Javier; Archer, Lynden A.
  • Macromolecules, Vol. 35, Issue 13
  • DOI: 10.1021/ma020321q

Generalized Cole-Cole behavior and its rheological relevance
journal, January 1992

Systems Manifesting Superposed Elastic and Viscous Behavior
journal, January 1945

  • Tobolsky, A. V.; Andrews, R. D.
  • The Journal of Chemical Physics, Vol. 13, Issue 1
  • DOI: 10.1063/1.1723966

A New Criterion for Expressing the ‘Intensity of Firmness’ of Soft Bodies
journal, October 1943

Relaxation in filled polymers: A fractional calculus approach
journal, October 1995

  • Metzler, Ralf; Schick, Winfried; Kilian, Hanns‐Georg
  • The Journal of Chemical Physics, Vol. 103, Issue 16
  • DOI: 10.1063/1.470346

Visco‐Elasticity of Rubber
journal, June 1951

  • Blizard, Robert B.
  • Journal of Applied Physics, Vol. 22, Issue 6
  • DOI: 10.1063/1.1700039

Rheology and Dynamics of Associative Polymers in Shear and Extension:  Theory and Experiments
journal, March 2006

  • Tripathi, Anubhav; Tam, Kam C.; McKinley, Gareth H.
  • Macromolecules, Vol. 39, Issue 5
  • DOI: 10.1021/ma051614x

Gesetze der elastischen Nachwirkung für constante Temperatur
journal, January 1893

Some phenomenological consequences of the Doi–Edwards theory of viscoelasticity
journal, January 1980

A kinetic theory for polymer melts VI. calculation of additional material functions
journal, January 1984

Chain Contraction and Change in Entanglement Structure of Well-Entangled Polymer in Large Shearing Deformations
journal, July 1995

  • Isono, Yoshinobu; Ohashi, Nobuyuki; Kase, Toshio
  • Macromolecules, Vol. 28, Issue 14
  • DOI: 10.1021/ma00118a053

Association behavior of end-functionalized polymers. 2. Melt rheology of polyisoprenes with carboxylate, amine, and zwitterion end groups
journal, November 1988

  • Fetters, Lewis J.; Graessley, William W.; Hadjichristidis, Nikos
  • Macromolecules, Vol. 21, Issue 6
  • DOI: 10.1021/ma00184a021

Stress relaxation of polymeric liquids after double-step strain
journal, September 1980

A strain stiffening theory for transient polymer networks under asymptotically nonlinear oscillatory shear
journal, July 2017

  • Bharadwaj, N. Ashwin; Schweizer, Kenneth S.; Ewoldt, Randy H.
  • Journal of Rheology, Vol. 61, Issue 4
  • DOI: 10.1122/1.4979368

Linear models of dissipation in anelastic solids
journal, April 1971

  • Caputo, M.; Mainardi, F.
  • La Rivista del Nuovo Cimento, Vol. 1, Issue 2
  • DOI: 10.1007/bf02820620

Defining nonlinear rheological material functions for oscillatory shear
journal, January 2013

A kinetic theory for polymer melts. I. The equation for the single‐link orientational distribution function
journal, February 1981

  • Curtiss, C. F.; Bird, R. Byron
  • The Journal of Chemical Physics, Vol. 74, Issue 3
  • DOI: 10.1063/1.441246

The relaxation time spectrum of nearly monodisperse polybutadiene melts
journal, January 1992

  • Baurngaertel, M.; De Rosa, M. E.; Machado, J.
  • Rheologica Acta, Vol. 31, Issue 1
  • DOI: 10.1007/bf00396469

A kinetic theory for polymer melts. II. The stress tensor and the rheological equation of state
journal, February 1981

  • Curtiss, C. F.; Bird, R. Byron
  • The Journal of Chemical Physics, Vol. 74, Issue 3
  • DOI: 10.1063/1.441247

Non‐Newtonian Viscoelastic Properties of Rod‐Like Macromolecules in Solution
journal, April 1956

  • Kirkwood, John G.; Plock, Richard J.
  • The Journal of Chemical Physics, Vol. 24, Issue 4
  • DOI: 10.1063/1.1742594

Simple shearing flows in polyisobutylene solutions
journal, January 1971

  • Zapas, L. J.; Phillips, J. C.
  • Journal of Research of the National Bureau of Standards Section A: Physics and Chemistry, Vol. 75A, Issue 1
  • DOI: 10.6028/jres.075a.005

Rouse–Bueche theory and the calculation of the monomeric friction coefficient in a filled system
journal, April 2016

  • Martinetti, Luca; Macosko, Christopher W.; Bates, Frank S.
  • Journal of Polymer Science Part B: Polymer Physics, Vol. 54, Issue 15
  • DOI: 10.1002/polb.24045

Nonlinear strain measures for general biaxial extension of polymer melts
journal, January 1992

  • Wagner, M. H.; Schaeffer, J.
  • Journal of Rheology, Vol. 36, Issue 1
  • DOI: 10.1122/1.550338

Melt rheology of some model comb polystyrenes
journal, May 1981

Stress Relaxation in Transient Networks of Symmetric Triblock Styrene−Isoprene−Styrene Copolymer
journal, January 2002

  • Hotta, A.; Clarke, S. M.; Terentjev, E. M.
  • Macromolecules, Vol. 35, Issue 1
  • DOI: 10.1021/ma001976z

Microgels: model polymers for the crosslinked state
journal, August 1990

  • Antonietti, Markus; Bremser, Wolfgang; Schmidt, Manfred
  • Macromolecules, Vol. 23, Issue 16
  • DOI: 10.1021/ma00218a014

Rheology of model polyurethanes at the gel point
journal, August 1986

  • Chambon, Francois; Petrovic, Zoran S.; MacKnight, William J.
  • Macromolecules, Vol. 19, Issue 8
  • DOI: 10.1021/ma00162a007

Dynamics of concentrated polymer systems. Part 3.—The constitutive equation
journal, January 1978

  • Doi, Masao; Edwards, S. F.
  • J. Chem. Soc., Faraday Trans. 2, Vol. 74, Issue 0
  • DOI: 10.1039/f29787401818

Hierarchical analogues to fractional relaxation equations
journal, October 1993

Large-amplitude oscillatory shear flow from the corotational Maxwell model
journal, October 2011

  • Giacomin, A. J.; Bird, R. B.; Johnson, L. M.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 166, Issue 19-20
  • DOI: 10.1016/j.jnnfm.2011.04.002

Nonlinear Viscoelastic Response of Amorphous Elastomers to Constant Strain Rates
journal, March 1962

  • Smith, Thor L.
  • Transactions of the Society of Rheology, Vol. 6, Issue 1
  • DOI: 10.1122/1.548933

Viscoelastic behavior of cubic phases in block copolymer melts
journal, January 1999

  • Kossuth, M. B.; Morse, D. C.; Bates, F. S.
  • Journal of Rheology, Vol. 43, Issue 1
  • DOI: 10.1122/1.550981

Observation of void formation patterns in SnAg films undergoing electromigration and simulation using random walk methods
journal, April 2021

Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers
journal, May 2011

  • Wagner, Manfred H.; Rolón-Garrido, Víctor Hugo; Hyun, Kyu
  • Journal of Rheology, Vol. 55, Issue 3
  • DOI: 10.1122/1.3553031

Mesoscopic Pictures of the Sol-Gel Transition: Ladder Models and Fractal Networks
journal, May 1995

Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential
journal, May 1996

  • Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.
  • Journal of Mathematical Physics, Vol. 37, Issue 5
  • DOI: 10.1063/1.531509

Explanation for the 3.4-power law for viscosity of polymeric liquids on the basis of the tube model
journal, May 1983

Significance of the Equation of State for Rubber
journal, May 1946

  • Guth, Eugene; Wack, Paul E.; Anthony, Robert L.
  • Journal of Applied Physics, Vol. 17, Issue 5
  • DOI: 10.1063/1.1707723

Unexpected power-law stress relaxation of entangled ring polymers
journal, October 2008

  • Kapnistos, M.; Lang, M.; Vlassopoulos, D.
  • Nature Materials, Vol. 7, Issue 12
  • DOI: 10.1038/nmat2292

Nonlinear Continuum Mechanics of Viscoelastic Fluids
journal, January 1971

The Irreversibility Assumption of Network Disentanglement in Flowing Polymer Melts and its Effects on Elastic Recoil Predictions
journal, August 1979

  • Wagner, M. H.; Stephenson, S. E.
  • Journal of Rheology, Vol. 23, Issue 4
  • DOI: 10.1122/1.549529

Constitutive equations for polymer melts predicted by the Doi—Edwards and Curtiss—Bird kinetic theory models
journal, January 1982

Modeling of oscillatory shear flow of emulsions under small and large deformation fields
journal, November 2002

  • Yu, Wei; Bousmina, Mosto; Grmela, Miroslav
  • Journal of Rheology, Vol. 46, Issue 6
  • DOI: 10.1122/1.1517303

Explanation for the 3.4 power law of viscosity of polymeric liquids on the basis of the tube model
journal, May 1981

Extensional and shear rheometry of oriented triblock copolymers
journal, August 2000

Dynamics of concentrated polymer systems. Part 2.—Molecular motion under flow
journal, January 1978

  • Doi, Masao; Edwards, S. F.
  • J. Chem. Soc., Faraday Trans. 2, Vol. 74, Issue 0
  • DOI: 10.1039/f29787401802

The mechanics of non-linear materials with memory: Part I
journal, January 1957

  • Green, A. E.; Rivlin, R. S.
  • Archive for Rational Mechanics and Analysis, Vol. 1, Issue 1
  • DOI: 10.1007/bf00297992

Tube theory of entangled polymer dynamics
journal, September 2002

Generalized viscoelastic models: their fractional equations with solutions
journal, December 1995

  • Schiessel, H.; Metzler, R.; Blumen, A.
  • Journal of Physics A: Mathematical and General, Vol. 28, Issue 23
  • DOI: 10.1088/0305-4470/28/23/012

New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear
journal, November 2008

  • Ewoldt, Randy H.; Hosoi, A. E.; McKinley, Gareth H.
  • Journal of Rheology, Vol. 52, Issue 6
  • DOI: 10.1122/1.2970095

From stretched exponential to inverse power-law: fractional dynamics, Cole–Cole relaxation processes, and beyond
journal, July 2002

A Constitutive Equation for Polymer Melts Based on Partially Extending Strand Convection
journal, October 1984

Are Polymer Melts Visco‐Anelastic?
journal, December 1986

  • Larson, R. G.; Valesano, V. A.
  • Journal of Rheology, Vol. 30, Issue 6
  • DOI: 10.1122/1.549882

The interchain pressure effect in shear rheology
journal, January 2010

On the Fractional Calculus Model of Viscoelastic Behavior
journal, February 1986

  • Bagley, R. L.; Torvik, P. J.
  • Journal of Rheology, Vol. 30, Issue 1
  • DOI: 10.1122/1.549887

Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework
journal, March 2018

  • Saengow, Chaimongkol; Giacomin, A. Jeffrey
  • Physics of Fluids, Vol. 30, Issue 3
  • DOI: 10.1063/1.5023586

The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear
journal, July 2014

  • Bharadwaj, N. Ashwin; Ewoldt, Randy H.
  • Journal of Rheology, Vol. 58, Issue 4
  • DOI: 10.1122/1.4874344

Evolution of time constants during sol-gel transition
journal, November 1989

  • Friedrich, C.; Heymann, L.; Berger, H. -R.
  • Rheologica Acta, Vol. 28, Issue 6
  • DOI: 10.1007/bf01332925

Recent Advances in the Molecular Aspects of Polymer Viscoelasticity
journal, July 1987

  • Pearson, Dale S.
  • Rubber Chemistry and Technology, Vol. 60, Issue 3
  • DOI: 10.5254/1.3536138

Viscoelastic properties of entangled flexible polymers
journal, January 1983

Effect of the Presence of Diblock Copolymer on the Nonlinear Elastic and Viscoelastic Properties of Elastomeric Triblock Copolymers
journal, September 2005

  • Roos, Alexandra; Creton, Costantino
  • Macromolecules, Vol. 38, Issue 18
  • DOI: 10.1021/ma050322t

New Interpretation of Shear Thickening in Telechelic Associating Polymers
journal, July 2015

Low-dimensional intrinsic material functions for nonlinear viscoelasticity
journal, March 2013

A geometrical interpretation of large amplitude oscillatory shear response
journal, May 2005

  • Cho, Kwang Soo; Hyun, Kyu; Ahn, Kyung Hyun
  • Journal of Rheology, Vol. 49, Issue 3
  • DOI: 10.1122/1.1895801

Constitutive model fingerprints in medium-amplitude oscillatory shear
journal, March 2015

  • Bharadwaj, N. Ashwin; Ewoldt, Randy H.
  • Journal of Rheology, Vol. 59, Issue 2
  • DOI: 10.1122/1.4903346

A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility
journal, January 1982

Relaxation of shear and normal stresses in step-shear deformation of a polystyrene solution. Comparison with the predictions of the Doi–Edwards theory
journal, March 1981

  • Osaki, Kunihiro; Kimura, Shinichi; Kurata, Michio
  • Journal of Polymer Science: Polymer Physics Edition, Vol. 19, Issue 3
  • DOI: 10.1002/pol.1981.180190312

An Additive Functional Theory of Viscoelastic Deformation with Application to Amorphous Polymers, Solutions and Vulcanizates
journal, March 1967

  • L. White, James; Tokita, Noboru
  • Journal of the Physical Society of Japan, Vol. 22, Issue 3
  • DOI: 10.1143/jpsj.22.719

Ultimate tensile properties of elastomers. I. Characterization by a time and temperature independent failure envelope
journal, December 1963

Linear viscoelastic behaviour of complex polymeric materials: a fractional mode representation
journal, December 1994

  • Friedrich, Chr; Braun, H.
  • Colloid & Polymer Science, Vol. 272, Issue 12
  • DOI: 10.1007/bf00664721

Rheological material functions for associating comb-shaped or H-shaped polymers A fractional calculus approach
journal, December 1992

Separability criteria for entangled polymer liquids
journal, November 1999

Step-strain deformations for viscoelastic fluids: Formulation of a strain-coupling constitutive equation
journal, April 1991

  • Vrentas, J. S.; Venerus, D. C.; Vrentas, C. M.
  • Journal of Polymer Science Part B: Polymer Physics, Vol. 29, Issue 5
  • DOI: 10.1002/polb.1991.090290503

Block copolymers near the microphase separation transition. 2. Linear dynamic mechanical properties
journal, December 1984

Calculation of the nonlinear stress of polymers in oscillatory shear fields
journal, July 1982

  • Helfand, Eugene; Pearson, Dale S.
  • Journal of Polymer Science: Polymer Physics Edition, Vol. 20, Issue 7
  • DOI: 10.1002/pol.1982.180200711

Linear viscoelastic behavior of densely grafted poly(chloroethyl vinyl ether)- g -polystyrene combs in the melt
journal, July 2003

  • Bailly, Christian; Stephenne, Vincent; Muchtar, Zainuddin
  • Journal of Rheology, Vol. 47, Issue 4
  • DOI: 10.1122/1.1579688

A model for the nonlinear rheology of associating polymers
journal, August 2000

A critical gel fluid with high extensibility: The rheology of chewing gum
journal, July 2014

  • Martinetti, Luca; Mannion, Alexander M.; Voje, William E.
  • Journal of Rheology, Vol. 58, Issue 4
  • DOI: 10.1122/1.4874322

Viscoelastic properties of physically crosslinked networks. 1. Transient network theory
journal, September 1992

Dynamics of Block Copolymers: Theory and Experiment
journal, January 1996

The damping function in rheology
journal, February 2009

Dynamics of polymeric fractals
journal, September 1985

  • Muthukumar, M.
  • The Journal of Chemical Physics, Vol. 83, Issue 6
  • DOI: 10.1063/1.449222

Step strain deformations for viscoelastic fluids: Experiment
journal, July 1990

  • Venerus, D. C.; Vrentas, C. M.; Vrentas, J. S.
  • Journal of Rheology, Vol. 34, Issue 5
  • DOI: 10.1122/1.550146

Connection between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties
journal, August 1994

  • Fetters, L. J.; Lohse, D. J.; Richter, D.
  • Macromolecules, Vol. 27, Issue 17
  • DOI: 10.1021/ma00095a001

A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
journal, December 2011

Molecular theory of the viscoelāstic properties of concentrated polymer solutions
journal, May 1974

Models of shear-thickening behavior in physically crosslinked networks
journal, November 1993

  • Marrucci, G.; Bhargava, S.; Cooper, S. L.
  • Macromolecules, Vol. 26, Issue 24
  • DOI: 10.1021/ma00076a027

Influence of the phase separation on the linear viscoelastic properties of a polystyrene-poly(vinyl methyl ether) blend
journal, September 1988

Molecular origins of higher harmonics in large-amplitude oscillatory shear flow: Shear stress response
journal, October 2016

  • Gilbert, P. H.; Giacomin, A. J.
  • Physics of Fluids, Vol. 28, Issue 10
  • DOI: 10.1063/1.4963101

An Integral Constitutive Equation for Mixed Flows: Viscoelastic Characterization
journal, August 1983

  • Papanastasiou, A. C.; Scriven, L. E.; Macosko, C. W.
  • Journal of Rheology, Vol. 27, Issue 4
  • DOI: 10.1122/1.549712

Linear Viscoelasticity at the Gel Point of a Crosslinking PDMS with Imbalanced Stoichiometry
journal, November 1987

  • Chambon, Francois; Winter, H. Henning
  • Journal of Rheology, Vol. 31, Issue 8
  • DOI: 10.1122/1.549955

Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress
journal, April 2017

  • Saengow, C.; Giacomin, A. J.; Kolitawong, C.
  • Physics of Fluids, Vol. 29, Issue 4
  • DOI: 10.1063/1.4978959

Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems
journal, July 1982

  • Osaki, Kunihiro; Nishizawa, Koji; Kurata, Michio
  • Macromolecules, Vol. 15, Issue 4
  • DOI: 10.1021/ma00232a021

Influence of phase separation on the linear viscoelastic behavior of a miscible polymer blend
journal, November 1992

  • Mani, Suresh; Malone, Michael F.; Winter, H. Henning
  • Journal of Rheology, Vol. 36, Issue 8
  • DOI: 10.1122/1.550277

Validity of separable BKZ model for large amplitude oscillatory shear
journal, September 1993

  • Giacomin, A. J.; Jeyaseelan, R. S.; Samurkas, T.
  • Journal of Rheology, Vol. 37, Issue 5
  • DOI: 10.1122/1.550396

Stress Relaxation of Polymer Solutions under Large Strain
journal, July 1971

  • Einaga, Yoshiyuki; Osaki, Kunihiro; Kurata, Michio
  • Polymer Journal, Vol. 2, Issue 4
  • DOI: 10.1295/polymj.2.550

Iterative Numerical Methods for Some Integral Equations Arising in Rheology
journal, March 1970

  • Tanner, R. I.; Williams, G.
  • Transactions of the Society of Rheology, Vol. 14, Issue 1
  • DOI: 10.1122/1.549160

Erratum: Foundations of Linear Viscoelasticity
journal, October 1964

The relaxation of polymers with linear flexible chains of uniform length
journal, September 1990

  • Baumgaertel, M.; Schausberger, A.; Winter, H. H.
  • Rheologica Acta, Vol. 29, Issue 5
  • DOI: 10.1007/bf01376790

Applications of Fractional Calculus to the Theory of Viscoelasticity
journal, June 1984

  • Koeller, R. C.
  • Journal of Applied Mechanics, Vol. 51, Issue 2
  • DOI: 10.1115/1.3167616

A model for viscoelastic fluid behavior which allows non-affine deformation
journal, May 1977

Brownian dynamics of self-similar macromolecules
journal, January 1985

Foam Rheology: III. Measurement of Shear Flow Properties
journal, January 1988

  • Khan, Saad A.; Schnepper, Carol A.; Armstrong, Robert C.
  • Journal of Rheology, Vol. 32, Issue 1
  • DOI: 10.1122/1.549964

A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
journal, June 1983

  • Bagley, R. L.; Torvik, P. J.
  • Journal of Rheology, Vol. 27, Issue 3
  • DOI: 10.1122/1.549724

Molecular rheology of concentrated polymer systems. I
journal, May 1980

A network theory of flow birefringence and stress in concentrated polymer solutions
journal, January 1956

Hierarchical models for viscoelasticity: dynamic behaviour in the linear range
journal, January 1996

Experimental Challenges of Shear Rheology: How to Avoid Bad Data
book, October 2014

Elastoviscous properties of polyisobutylene (and other amorphous polymers) from stress–relaxation studies. IX. A summary of results
journal, January 1956

Non‐Newtonian Viscoelastic Properties of Rodlike Molecules in Solution: Comment on a Paper by Kirkwood and Plock
journal, August 1969

Systems Manifesting Superposed Elastic and Viscous Behavior
journal, December 1945

  • Tobolsky, A. V.; Andrews, R. D.
  • Rubber Chemistry and Technology, Vol. 18, Issue 4
  • DOI: 10.5254/1.3546773

Some Nonlinear Viscoelastic Models with Inclusion of Results from Molecular Theory
journal, May 1965

  • Spriggs, T. W.; Bird, R. B.
  • Industrial & Engineering Chemistry Fundamentals, Vol. 4, Issue 2
  • DOI: 10.1021/i160014a015

Viscoelastic properties of rubber-modified polymeric materials at elevated temperatures
journal, January 1984

  • Masuda, T.; Nakajima, A.; Kitamura, M.
  • Pure and Applied Chemistry, Vol. 56, Issue 10
  • DOI: 10.1351/pac198456101457

Extension of a Model for Crosslinking Polymer at the Gel Point
journal, April 1988

  • Friedrich, Chr.; Heymann, L.
  • Journal of Rheology, Vol. 32, Issue 3
  • DOI: 10.1122/1.549971

Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields
journal, January 1982

  • Pearson, Dale S.; Rochefort, Willie E.
  • Journal of Polymer Science: Polymer Physics Edition, Vol. 20, Issue 1
  • DOI: 10.1002/pol.1982.180200107

Dynamics of concentrated polymer systems. Part 4.—Rheological properties
journal, January 1979

  • Doi, Masao; Edwards, S. F.
  • J. Chem. Soc., Faraday Trans. 2, Vol. 75, Issue 0
  • DOI: 10.1039/f29797500038

Analysis of Linear Viscoelasticity of a Crosslinking Polymer at the Gel Point
journal, April 1986

  • Winter, H. Henning; Chambon, Francois
  • Journal of Rheology, Vol. 30, Issue 2
  • DOI: 10.1122/1.549853

A four-constant model for viscoelastic fluids
journal, November 1965

On the damping function of shear relaxation modulus for entangled polymers
journal, January 1993

Fractal rheological models and fractional differential equations for viscoelastic behavior
journal, January 1994

  • Heymans, Nicole; Bauwens, J. -C.
  • Rheologica Acta, Vol. 33, Issue 3
  • DOI: 10.1007/bf00437306

A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers
journal, July 1953

  • Rouse, Prince E.
  • The Journal of Chemical Physics, Vol. 21, Issue 7
  • DOI: 10.1063/1.1699180

Dynamics of Entangled Solutions of Associating Polymers
journal, February 2001

  • Rubinstein, Michael; Semenov, Alexander N.
  • Macromolecules, Vol. 34, Issue 4
  • DOI: 10.1021/ma0013049

Inferring the Nonlinear Mechanisms of a Reversible Network
journal, October 2018

Elastoviscous properties of polyisobutylene. I. Relaxation of stress in whole polymer of different molecular weights at elevated temperatures
journal, October 1948

Dynamic mechanical measurement of crystallization-induced gelation in thermoplastic elastomeric poly(propylene)
journal, July 1991

  • Lin, Y. G.; Mallin, D. T.; Chien, J. C. W.
  • Macromolecules, Vol. 24, Issue 4
  • DOI: 10.1021/ma00004a006

On the thermodynamics of fractional damping elements
journal, April 1997

Nonlinear Dynamic Mechanical Moduli for Polycarbonate and PMMA
journal, February 1978

  • Davis, W. M.; Macosko, C. W.
  • Journal of Rheology, Vol. 22, Issue 1
  • DOI: 10.1122/1.549500

Nonlinear Viscoelastic Response of Amorphous Elastomers to Constant Strain Rates
journal, July 1963

  • Smith, Thor L.
  • Rubber Chemistry and Technology, Vol. 36, Issue 3
  • DOI: 10.5254/1.3539599

Ultimate Tensile Properties of Elastomers. I. Characterization by a Time and Temperature Independent Failure Envelope
journal, September 1964

  • Smith, Thor L.
  • Rubber Chemistry and Technology, Vol. 37, Issue 4
  • DOI: 10.5254/1.3540377

The phenomenological theory of linear viscoelastic behavior
journal, November 1990

Rheology of Soft Glassy Materials
text, January 1996

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    The medium amplitude response of nonlinear Maxwell–Oldroyd type models in simple shear
    journal, September 2021

    • Lennon, Kyle R.; McKinley, Gareth H.; Swan, James W.
    • Journal of Non-Newtonian Fluid Mechanics, Vol. 295
    • DOI: 10.1016/j.jnnfm.2021.104601
      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: