Can simulated waveform (using estimated G₁′, G₃′, G₅′) be used as valid input for MITlaos analysis?

23 June 2025 1 5K Report

Dear Colleagues. I am currently working on LAOS (Large Amplitude Oscillatory Shear) characterization using an experiment. However, we are only able to extract amplitude sweep data (G′, G″ vs strain amplitude) — not the full shear stress vs time waveform.

Since tools like MITlaos require time-resolved waveforms to extract nonlinear contributions (e.g., G₃′, G₅′), I am exploring whether MATLAB can be used to simulate the shear stress waveform based on amplitude sweep data and estimated higher harmonics.

Questions:

Has anyone successfully reconstructed shear stress waveforms in MATLAB using only amplitude sweep data?

Can the simulated waveform (using known or estimated G₁′, G₃′, G₅′) be used as valid input for MITlaos analysis?

Are there any publications, or examples you could recommend for this simulation approach?

Any guidance, or references would be highly appreciated. Thank you in advance for your insights.

Best regards, Kiran

Farid Leguebedj

In principle, yes, a simulated waveform using estimated values of G1′G_1′G1′, G3′G_3′G3′, and G5′G_5′G5′ (the elastic moduli from LAOS analysis) can be used as an input for MITlaos, but with important caveats.

✅ When it is valid:

Purpose is educational or exploratory: If you're using MITlaos (an open-source tool for Large Amplitude Oscillatory Shear analysis) to test how G1′G_1′G1′, G3′G_3′G3′, G5′G_5′G5′ affect the waveform and interpret nonlinear rheology behavior.

Your simulated waveform is constructed to match the expected form:σ(t)=γ0[G1′sin⁡(ωt)+G3′sin⁡(3ωt)+G5′sin⁡(5ωt)+… ]\sigma(t) = \gamma_0 \left[ G_1′ \sin(\omega t) + G_3′ \sin(3\omega t) + G_5′ \sin(5\omega t) + \dots \right]σ(t)=γ0[G1′sin(ωt)+G3′sin(3ωt)+G5′sin(5ωt)+…] In LAOS, the stress response σ(t)\sigma(t)σ(t) to a sinusoidal strain γ(t)=γ0sin⁡(ωt)\gamma(t) = \gamma_0 \sin(\omega t)γ(t)=γ0sin(ωt) is typically: If your simulated waveform is built from such a sum with appropriate harmonics and scaling, it can be used.

Waveform is formatted correctly: MITlaos expects time-series input in a specific format (e.g., strain and stress vs. time in .txt or .csv format).

⚠️ When it is not valid:

If used for inverse analysis or parameter extraction: MITlaos is designed to extract G1′G_1′G1′, G3′G_3′G3′, etc., from experimental waveforms. Feeding it a simulated waveform that’s already constructed from assumed Gn′G_n′Gn′ defeats the purpose of inversion.

If the waveform lacks noise or realistic features: Real experimental data include noise, instrument effects, and non-idealities. A simulated waveform may give misleadingly “perfect” results, not reflective of real material behavior.

Improper phase relations or missing viscous components: LAOS involves both elastic and viscous nonlinearities. If you only simulate in-phase elastic terms (Gn′G_n′Gn′) and omit the out-of-phase viscous terms (Gn″G_n″Gn″), the input may be incomplete for full analysis.

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