A full understanding of the sequence of processes exhibited by yield stress fluids under large amplitude oscillatory shearing is developed using multiple experimental and analytical approaches. A novel component rate Lissajous curve, where the rates at which strain is acquired unrecoverably and recoverably are plotted against each other, is introduced and its utility is demonstrated by application to the analytical responses of four simple viscoelastic models. Using the component rate space, yielding and unyielding are identified by changes in the way strain is acquired, from recoverably to unrecoverably and back again. The behaviors are investigated by comparing the experimental results with predictions from the elastic Bingham model that is constructed using the Oldroyd–Prager formalism and the recently proposed continuous model by Kamani, Donley, and Rogers in which yielding is enhanced by rapid acquisition of elastic strain. The physical interpretation gained from the transient large amplitude oscillatory shear (LAOS) data is compared to the results from the analytical sequence of physical processes framework and a novel time-resolved Pipkin space. The component rate figures, therefore, provide an independent test of the interpretations of the sequence of physical processes analysis that can also be applied to other LAOS analysis frameworks. Each of these methods, the component rates, the sequence of physical processes analysis, and the time-resolved Pipkin diagrams, unambigiously identifies the same material physics, showing that yield stress fluids go through a sequence of physical processes that includes elastic deformation, gradual yielding, plastic flow, and gradual unyielding.

1.
Bonn
,
D.
,
H.
Tanaka
,
G.
Wegdam
,
H.
Kellay
, and
J.
Meunier
, “
Aging of a colloidal ‘Wigner’ glass
,”
Europhys. Lett.
45
,
52
57
(
1999
).
2.
Burmistrova
,
A.
, and
R.
von Klitzing
, “
Control of number density and swelling/shrinking behavior of P (NIPAM–AAc) particles at solid surfaces
,”
J. Mater. Chem.
20
,
3502
3507
(
2010
).
3.
Clasen
,
C.
,
B. P.
Gearing
, and
G. H.
McKinley
, “
The flexure-based microgap rheometer (FMR)
,”
J. Rheol.
50
,
883
905
(
2006
).
4.
Cloitre
,
M.
,
R.
Borrega
,
F.
Monti
, and
L.
Leibler
, “
Glassy dynamics and flow properties of soft colloidal pastes
,”
Phys. Rev. Lett.
90
,
068303
(
2003
).
5.
Jalaal
,
M.
,
G.
Cottrell
,
N.
Balmforth
, and
B.
Stoeber
, “
On the rheology of pluronic f127 aqueous solutions
,”
J. Rheol.
61
,
139
146
(
2017
).
6.
Jiang
,
T.
, and
C. F.
Zukoski
, “
Rheology of high density glass of binary colloidal mixtures in unentangled polymer melts
,”
Soft Matter
9
,
3117
3130
(
2013
).
7.
Kramb
,
R. C.
, and
C. F.
Zukoski
, “
Nonlinear rheology and yielding in dense suspensions of hard anisotropic colloids
,”
J. Rheol.
55
,
1069
1084
(
2011
).
8.
Le Merrer
,
M.
,
R.
Lespiat
,
R.
Höhler
, and
S.
Cohen-Addad
, “
Linear and non-linear wall friction of wet foams
,”
Soft Matter
11
,
368
381
(
2015
).
9.
Nordstrom
,
K. N.
,
E.
Verneuil
,
P.
Arratia
,
A.
Basu
,
Z.
Zhang
,
A. G.
Yodh
,
J. P.
Gollub
, and
D. J.
Durian
, “
Microfluidic rheology of soft colloids above and below jamming
,”
Phys. Rev. Lett.
105
,
175701
(
2010
).
10.
O’Bryan
,
C. S.
,
T.
Bhattacharjee
,
S.
Hart
,
C. P.
Kabb
,
K. D.
Schulze
,
I.
Chilakala
,
B. S.
Sumerlin
,
W. G.
Sawyer
, and
T. E.
Angelini
, “
Self-assembled micro-organogels for 3D printing silicone structures
,”
Sci. Adv.
3
,
e1602800
(
2017
).
11.
Piau
,
J.-M.
, “
Carbopol gels: Elastoviscoplastic and slippery glasses made of individual swollen sponges: Meso-and macroscopic properties, constitutive equations and scaling laws
,”
J. Non-Newtonian Fluid Mech.
144
,
1
29
(
2007
).
12.
Rogers
,
S. A.
,
B. M.
Erwin
,
D.
Vlassopoulos
, and
M.
Cloitre
, “
A sequence of physical processes determined and quantified in LAOS: Application to a yield stress fluid
,”
J. Rheol.
55
,
435
458
(
2011
).
13.
Senff
,
H.
, and
W.
Richtering
, “
Temperature sensitive microgel suspensions: Colloidal phase behavior and rheology of soft spheres
,”
J. Chem. Phys.
111
,
1705
1711
(
1999
).
14.
Ginder
,
J. M.
,
L. C.
Davis
, and
L. D.
Elie
, “
Rheology of magnetorheological fluids: Models and measurements
,”
Int. J. Mod. Phys. B
10
,
3293
3303
(
1996
).
15.
Liu
,
X.
,
J.
Guo
,
Y.
Cheng
,
G.
Xu
,
Y.
Li
, and
P.
Cui
, “
Synthesis and electrorheological properties of polar molecule-dominated tio 2 particles with high yield stress
,”
Rheol. Acta
236
,
96
103
(
2010
).
16.
Liu
,
Y. D.
, and
H. J.
Choi
, “
Electrorheological fluids: Smart soft matter and characteristics
,”
Soft Matter
8
,
11961
11978
(
2012
).
17.
Mickel
,
W.
,
S.
Münster
,
L. M.
Jawerth
,
D. A.
Vader
,
D. A.
Weitz
,
A. P.
Sheppard
,
K.
Mecke
,
B.
Fabry
, and
G. E.
Schröder-Turk
, “
Robust pore size analysis of filamentous networks from three-dimensional confocal microscopy
,”
Biophys. J.
95
,
6072
6080
(
2008
).
18.
Patel
,
A. R.
,
B.
Mankoč
,
M. D.
Bin Sintang
,
A.
Lesaffer
, and
K.
Dewettinck
, “
Fumed silica-based organogels and ‘aqueous-organic’ bigels
,”
RSC Adv.
5
,
9703
9708
(
2015
).
19.
Rankin
,
P. J.
,
A. T.
Horvath
, and
D. J.
Klingenberg
, “
Magnetorheology in viscoplastic media
,”
Rheol. Acta
38
,
471
477
(
1999
).
20.
Walls
,
H. J.
,
S. B.
Caines
,
A. M.
Sanchez
, and
S. A.
Khan
, “
Yield stress and wall slip phenomena in colloidal silica gels
,”
J. Rheol.
47
,
847
868
(
2003
).
21.
Yang
,
H. G.
,
C. Z.
Li
,
H. C.
Gu
, and
T. N.
Fang
, “
Rheological behavior of titanium dioxide suspensions
,”
J. Colloid Interface Sci.
236
,
96
103
(
2001
).
22.
Zukoski
,
C. F.
, and
D. J.
Klingenberg
, “
Studies on the steady-shear behavior of electrorheological suspensions
,”
Langmuir
6
,
15
24
(
1990
).
23.
Bingham
,
E. C.
, “
An investigation of the laws of plastic flow
,”
Bull. Bureau Stand.
13
,
309
353
(
1916
).
24.
Bingham
,
E. C.
,
Fluidity and Plasticity
(
McGraw-Hill
,
New York
,
1922
), Vol. 2.
25.
Herschel
,
W. H.
, and
R.
Bulkley
, “
Konsistenzmessungen von gummi-benzollösungen
,”
Kolloid Z.
39
,
291
300
(
1926
).
26.
Casson
,
N.
, “Flow equation for pigment oil suspensions of the printing ink type,” in Rheology of Disperse Systems (Wiley, 1959), pp. 84–102.
27.
Oldroyd
,
J. G.
, “A rational formulation of the equations of plastic flow for a bingham solid,” in Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge University, Cambridge, 1947), Vol. 43, pp. 100–105.
28.
Hohenemser
,
K. V.
, and
W.
Prager
, “
Über die ansätze der mechanik isotroper kontinua
,”
J. Appl. Math. Mech.
12
,
216
226
(
1932
).
29.
Prager
,
W.
,
Introduction to Mechanics of Continua
(
Ginn & Co.
,
Boston
,
1961
).
30.
Saramito
,
P.
, “
A new constitutive equation for elastoviscoplastic fluid flows
,”
J. Non-Newtonian Fluid Mech.
145
,
1
14
(
2007
).
31.
Saramito
,
P.
, “
A new elastoviscoplastic model based on the Herschel–Bulkley viscoplastic model
,”
J. Non-Newtonian Fluid Mech.
158
,
154
161
(
2009
).
32.
Barnes
,
H.
, and
K.
Walters
, “
The yield stress myth?
,”
Rheol. Acta
24
,
323
326
(
1985
).
33.
Astarita
,
G.
, “
The engineering reality of the yield stress
,”
J. Rheol.
34
,
275
277
(
1990
).
34.
Dinkgreve
,
M.
,
J.
Paredes
,
M. M.
Denn
, and
D.
Bonn
, “
On different ways of measuring ‘the’ yield stress
,”
J. Non-Newtonian Fluid Mech.
238
,
233
241
(
2016
).
35.
Fernandes
,
R. R.
,
D. E.
Andrade
,
A. T.
Franco
, and
C. O.
Negrão
, “
The yielding and the linear-to-nonlinear viscoelastic transition of an elastoviscoplastic material
,”
J. Rheol.
61
,
893
903
(
2017
).
36.
Pignon
,
F.
,
A.
Magnin
, and
J.-M.
Piau
, “
Thixotropic colloidal suspensions and flow curves with minimum: Identification of flow regimes and rheometric consequences
,”
J. Rheol.
40
,
573
587
(
1996
).
37.
Møller
,
P.
,
S.
Rodts
,
M.
Michels
, and
D.
Bonn
, “
Shear banding and yield stress in soft glassy materials
,”
Phys. Rev. E
77
,
041507
(
2008
).
38.
Coussot
,
P.
, “
Slow flows of yield stress fluids: Yielding liquids or flowing solids?
,”
Rheol. Acta
57
,
1
14
(
2018
).
39.
Bécu
,
L.
,
S.
Manneville
, and
A.
Colin
, “
Yielding and flow in adhesive and nonadhesive concentrated emulsions
,”
Phys. Rev. Lett.
96
,
138302
(
2006
).
40.
Divoux
,
T.
,
D.
Tamarii
,
C.
Barentin
,
S.
Teitel
, and
S.
Manneville
, “
Yielding dynamics of a Herschel–Bulkley fluid: A critical-like fluidization behaviour
,”
Soft Matter
8
,
4151
4164
(
2012
).
41.
Gibaud
,
T.
,
C.
Barentin
, and
S.
Manneville
, “
Influence of boundary conditions on yielding in a soft glassy material
,”
Phys. Rev. Lett.
101
,
258302
(
2008
).
42.
Gibaud
,
T.
,
D.
Frelat
, and
S.
Manneville
, “
Heterogeneous yielding dynamics in a colloidal gel
,”
Soft Matter
6
,
3482
3488
(
2010
).
43.
Hébraud
,
P.
,
F.
Lequeux
,
J.
Munch
, and
D.
Pine
, “
Yielding and rearrangements in disordered emulsions
,”
Phys. Rev. Lett.
78
,
4657
4660
(
1997
).
44.
Knowlton
,
E. D.
,
D. J.
Pine
, and
L.
Cipelletti
, “
A microscopic view of the yielding transition in concentrated emulsions
,”
Soft Matter
10
,
6931
6940
(
2014
).
45.
Rogers
,
M. C.
,
K.
Chen
,
L.
Andrzejewski
,
S.
Narayanan
,
S.
Ramakrishnan
,
R. L.
Leheny
, and
J. L.
Harden
, “
Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear
,”
Phys. Rev. E
90
,
062310
(
2014
).
46.
Rogers
,
M. C.
,
K.
Chen
,
M. J.
Pagenkopp
,
T. G.
Mason
,
S.
Narayanan
,
J. L.
Harden
, and
R. L.
Leheny
, “
Microscopic signatures of yielding in concentrated nanoemulsions under large-amplitude oscillatory shear
,”
Phys. Rev. Mater.
2
,
095601
(
2018
).
47.
Gemant
,
A.
, “
A method of analyzing experimental results obtained from elasto-viscous bodies
,”
Physics
7
,
311
317
(
1936
).
48.
Ferry
,
J. D.
,
Viscoelastic Properties of Polymers
(
Wiley
,
New York
,
1980
).
49.
Tschoegl
,
N. W.
,
The Phenomenological Theory of Linear Viscoelastic Behavior
(
Springer
,
New York
,
1989
), pp. 314–364.
50.
Hyun
,
K.
,
S. H.
Kim
,
K. H.
Ahn
, and
S. J.
Lee
, “
Large amplitude oscillatory shear as a way to classify the complex fluids
,”
J. Non-Newtonian Fluid Mech.
107
,
51
65
(
2002
).
51.
Hyun
,
K.
,
M.
Wilhelm
,
C. O.
Klein
,
K. S.
Cho
,
J. G.
Nam
,
K. H.
Ahn
,
S. J.
Lee
,
R. H.
Ewoldt
, and
G. H.
McKinley
, “
A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
,”
Prog. Polym. Sci.
36
,
1697
1753
(
2011
).
52.
Kamkar
,
M.
,
R.
Salehyian
,
T. B.
Goudoulas
,
M.
Abbasi
,
C.
Saengow
,
E.
Erfanian
,
S.
Sadeghi
,
G.
Natale
,
S. A.
Rogers
,
A. J.
Giacomin
, and
U.
Sundararaj
, “
Large amplitude oscillatory shear flow: Microstructural assessment of polymeric systems
,”
Prog. Polym. Sci.
132
,
101580
(
2022
).
53.
Philippoff
,
W.
, “
Vibrational measurements with large amplitudes
,”
Trans. Soc. Rheol.
10
,
317
334
(
1966
).
54.
Dodge
,
J. S.
, and
I. M.
Krieger
, “
Oscillatory shear of nonlinear fluids I. Preliminary investigation
,”
Trans. Soc. Rheol.
15
,
589
601
(
1971
).
55.
Harris
,
J.
, and
K.
Bogie
, “
The experimental analysis of non-linear waves in mechanical systems
,”
Rheol. Acta
6
,
3
5
(
1967
).
56.
MacSporran
,
W.
, and
R.
Spiers
, “
The dynamic performance of the Weissenburg rheogoniometer I. Small amplitude oscillatory shearing
,”
Rheol. Acta
21
,
184
192
(
1982
).
57.
Tee
,
T.-T.
, and
J.
Dealy
, “
Nonlinear viscoelasticity of polymer melts
,”
J. Rheol.
19
,
595
615
(
1975
).
58.
Onogi
,
S.
,
T.
Masuda
, and
T.
Matsumoto
, “
Non-linear behavior of viscoelastic materials. I. Disperse systems of polystyrene solution and carbon black
,”
J. Rheol.
14
,
275
294
(
1970
).
59.
Pearson
,
D. S.
, and
W. E.
Rochefort
, “
Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields
,”
J. Polym. Sci.
20
,
83
98
(
1982
).
60.
Cho
,
K. S.
,
K.
Hyun
,
K. H.
Ahn
, and
S. J.
Lee
, “
A geometrical interpretation of large amplitude oscillatory shear response
,”
J. Rheol.
49
,
747
758
(
2005
).
61.
Yu
,
W.
,
P.
Wang
, and
C.
Zhou
, “
General stress decomposition in nonlinear oscillatory shear flow
,”
J. Rheol.
53
,
215
238
(
2009
).
62.
Ewoldt
,
R. H.
,
A.
Hosoi
, and
G. H.
McKinley
, “
New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear
,”
J. Rheol.
52
,
1427
1458
(
2008
).
63.
Klein
,
C. O.
,
H. W.
Spiess
,
A.
Calin
,
C.
Balan
, and
M.
Wilhelm
, “
Separation of the nonlinear oscillatory response into a superposition of linear, strain hardening, strain softening, and wall slip response
,”
Macromolecules
40
,
4250
4259
(
2007
).
64.
Rogers
,
S. A.
, and
M. P.
Lettinga
, “
A sequence of physical processes determined and quantified in LAOS: Application to theoretical nonlinear models
,”
J. Rheol.
56
,
1
25
(
2012
).
65.
Lee
,
C.-W.
, and
S. A.
Rogers
, “
A sequence of physical processes quantified in LAOS by continuous local measures
,”
Korea Aust. Rheol. J.
29
,
269
279
(
2017
).
66.
Choi
,
J.
,
F.
Nettesheim
, and
S. A.
Rogers
, “
The unification of disparate rheological measures in oscillatory shearing
,”
Phys. Fluids
31
,
073107
(
2019
).
67.
Donley
,
G. J.
,
J. R.
de Bruyn
,
G. H.
McKinley
, and
S. A.
Rogers
, “
Time-resolved dynamics of the yielding transition in soft materials
,”
J. Non-Newtonian Fluid Mech.
264
,
117
134
(
2019
).
68.
Donley
,
G. J.
,
W. W.
Hyde
,
S. A.
Rogers
, and
F.
Nettesheim
, “
Yielding and recovery of conductive pastes for screen printing
,”
Rheol. Acta
58
,
361
382
(
2019
).
69.
Rogers
,
S. A.
,
J. D.
Park
, and
C.-W. J.
Lee
, “
Instantaneous dimensionless numbers for transient nonlinear rheology
,”
Rheol. Acta
58
,
539
556
(
2019
).
70.
Rogers
,
S. A.
, “
In search of physical meaning: Defining transient parameters for nonlinear viscoelasticity
,”
Rheol. Acta
56
,
501
525
(
2017
).
71.
Pipkin
,
A. C.
,
Lectures on Viscoelasticity Theory
(
Springer
,
NewYork
,
1972
).
72.
Reiner
,
M.
, “
The Deborah number
,”
Phys. Today
17
(
1
),
62
(
1964
).
73.
Poole
,
R.
, “
The Deborah and Weissenberg numbers
,”
Rheol. Bull.
53
,
32
39
(
2012
).
74.
White
,
J. L.
, “
Dynamics of viscoelastic fluids, melt fracture, and the rheology of fiber spinning
,”
J. Appl. Polym. Sci.
8
,
2339
2357
(
1964
).
75.
Donley
,
G. J.
,
P. K.
Singh
,
A.
Shetty
, and
S. A.
Rogers
, “
Elucidating the g overshoot in soft materials with a yield transition via a time-resolved experimental strain decomposition
,”
Proc. Natl. Acad. Sci. U.S.A.
117
,
21945
21952
(
2020
).
76.
Weissenberg
,
K.
, “
A continuum theory of rheological phenomena
,”
Nature
159
,
310
311
(
1947
).
77.
Reiner
,
M.
,
Elasticity and Plasticity
(
Springer
,
New York
,
1958
).
78.
Singh
,
P. K.
,
J. C.-W.
Lee
,
K. A.
Patankar
, and
S. A.
Rogers
, “
Revisiting the basis of transient rheological material functions: Insights from recoverable strain measurements
,”
J. Rheol.
65
,
129
144
(
2021
).
79.
Lee
,
J. C.-W.
,
K. M.
Weigandt
,
E. G.
Kelley
, and
S. A.
Rogers
, “
Structure-property relationships via recovery rheology in viscoelastic materials
,”
Phys. Rev. Lett.
122
,
248003
(
2019
).
80.
Lee
,
J. C.-W.
,
Y.-T.
Hong
,
K. M.
Weigandt
,
E. G.
Kelley
,
H.
Kong
, and
S. A.
Rogers
, “
Strain shifts under stress-controlled oscillatory shearing in theoretical, experimental, and structural perspectives: Application to probing zero-shear viscosity
,”
J. Rheol.
63
,
863
881
(
2019
).
81.
Kamani
,
K.
,
G. J.
Donley
, and
S. A.
Rogers
, “
Unification of the rheological physics of yield stress fluids
,”
Phys. Rev. Lett.
126
,
218002
(
2021
).
82.
Yoshimura
,
A.
, and
R.
Prud’homme
, “
Response of an elastic bingham fluid to oscillatory shear
,”
Rheol. Acta
26
,
428
436
(
1987
).
83.
Coussot
,
P.
, and
S. A.
Rogers
, “
Oldroyd’s model and the foundation of modern rheology of yield stress fluids
,”
J. Non-Newtonian Fluid Mech.
295
,
104604
(
2021
).
84.
Ovarlez
,
G.
,
S.
Cohen-Addad
,
K.
Krishan
,
J.
Goyon
, and
P.
Coussot
, “
On the existence of a simple yield stress fluid behavior
,”
J. Non-Newtonian Fluid Mech.
193
,
68
79
(
2013
).
85.
Dimitriou
,
C. J.
, and
G. H.
McKinley
, “
A canonical framework for modeling elasto-viscoplasticity in complex fluids
,”
J. Non-Newtonian Fluid Mech.
265
,
116
132
(
2019
).
86.
Donley
,
G. J.
,
P. K.
Singh
,
A.
Shetty
, and
S. A.
Rogers
, “
Dataset for elucidating the g overshoot in soft materials with a yield transition via a time-resolved experimental strain decomposition
” (
2020
).
87.
Lee
,
J. C.-W.
,
L.
Porcar
, and
S. A.
Rogers
, “
Unveiling temporal nonlinear structure–rheology relationships under dynamic shearing
,”
Polymers
11
,
1189
1205
(
2019
).
88.
Park
,
J. D.
, and
S. A.
Rogers
, “
The transient behavior of soft glassy materials far from equilibrium
,”
J. Rheol.
62
,
869
888
(
2018
).
89.
Park
,
J. D.
, and
S. A.
Rogers
, “
Rheological manifestation of microstructural change of colloidal gel under oscillatory shear flow
,”
Phys. Fluids
32
,
063102
(
2020
).
You do not currently have access to this content.