Large Amplitude Oscillatory Shear (LAOS): An Emerging Technique that will Expand our view of Viscoelasticity

January 11, 2018

Large amplitude oscillatory shear (LAOS) is the rheology technique of the future that will revolutionize viscoelastic measurements once the data output can be interpreted with more clarity. Here is a brief synopsis of what has been accomplished by theorists and experimentalists to bring this method to mainstream rheometry, along with the steps needed to transform LAOS into a practical tool.



Going beyond the linear viscoelastic range (LVE) of strain will open many doors for applied testing. Gels and other soft solids could be examined with LAOS to show the behavior under large strains, such as polymer extrusion. Processing steps that employ repeated deformation of the sample could potentially be better simulated with LAOS measurements than regular rheometry due to varying both strain and frequency. (1) Additionally, colloids and suspensions that are prone to sedimentation under low-shear may be better evaluated with the high-shear of LAOS to prevent sedimentation from influencing the data. (2)


Past research on the post-LVE domains of amplitude sweeps (Figure 1) has lacked a standard interpretation, which led rheologists to present high strain data in terms of Lissajous plots. The example shown in Figure 2 portrays a stress vs. strain plot for a solid-like (elastic) sample next to a plot of stress vs. shear rate for a more liquid-like (viscous) sample.  A liquid without any solid-like characteristics would have a circle on the Lissajous plot, while a perfect solid would be shown as a diagonal line. For micellar solutions, it was shown that the Lissajous plots change drastically based on concentration. (3)  In this case, the LAOS data revealed a strain-specific colloidal structural transition that was not capable of being measured with traditional rheometry methods. (3)



Elastic modulus (G’) and viscous modulus (G”) together give us the degree of viscoelasticity, but when considered separately they are simply a degree of solid-like or liquid-like characteristics. LAOS measurements also give the third harmonic, which is a measure of viscoelasticity in of itself.  It is displayed as the “viscoelastic” stress divided into an elastic (τ’) and viscous (τ”) components. Secant and tangent slopes from the Lissajous plots also serve as values for comparison between samples.



Stress-strain waveform analysis has also emerged as a method for categorizing sample behavior under high strain. Shown in the example in Figure 3, a sinusoidal strain is maintained while the stress response not only displays an offset from the strain, but also has a contorted shape. The stress waveform shape can give many insights to differences within similar types of materials. For instance, two solutions with different surfactants displayed very different stress responses; one had a boxy stress wave while the other displayed distorted peaks. (1)


Correlations between Lissajous plots, waveforms, and viscoelastic stress to the structure and composition of the specimens are one of the most challenging aspects of LAOS data interpretation. Although many studies have defined structural differences between a specific set of samples based on LAOS data, a universal guide to charting results has yet to be composed. To get a strong understanding of high strain impact, researchers utilized SANs into their rheology to simultaneously track structural changes with the rheology.  (4) The structure-tracking results were then used to correlate LAOS data into a physical context for matching the graphs to structural breakdown.


The expansive work currently being undertaken to better understand LAOS will soon culminate for the benefit of applied industrial rheology. In order to reap the insights from LAOS studies, applied rheologists should be open-minded to expanding their view of oscillatory variables. Measurements of τ’ and τ” will show us the complexity of viscoelasticity, but they will also allow us to differentiate previously congruent deformation behaviors. Do not let the obscurities of LAOS turn you away – this method will become a powerful means for saving time and money for soft material product development.


To learn more about rheometry techniques for your own use, contact us for a free 30 minute consultation. 



  1.  Hyun, K., et al., “A Review of Nonlinear Oscillatory Shear Tests: Analysis and Application of Large Amplitude Oscillatory Shear (LAOS)”, Progress in Polymer Science, 2011, 36, 12, 1697.

  2. Sousa, P., et al., “Shear viscosity and nonlinear behavior of whole blood under large amplitude oscillatory shear”, Biorheology, 2013, 50, 269.

  3. Poulos, A., Stellbrink, J., and Petekidis, G., “Flow of concentrated solutions of starlike micelles under large-amplitude oscillatory shear”, Rheologica Acta, 2013, 52, 8, 785.

  4. Kim, J., et al., “The microstructure and rheology of a model, thixotropic nanoparticle gel under steady shear and large amplitude oscillatory shear (LAOS)”, Journal of Rheology, 2014, 58, 5, 1301.











Please reload

Our Recent Posts

Please reload


Please reload


Please reload

Murray Rheology Blog

©2017 by Murray Rheology Consulting. Proudly created with