LAOS: General Description

Purpose

The LAOS application provides views for the raw time signal, Lissajous plots, Fourier-based reconstructions, and Chebyshev analysis. The views use the three columns of a .laos file: time, strain, and stress. The file parameters omega and gamma are also required; omega is used when the view needs the strain-rate or harmonic frequencies.

This application is inspired by the software MITlaos.

Data Files

  • The first line of the file should contain the sample parameters separated by semi-colons (;). It may contain any number of parameters which will be read and saved as file-parameter in RepTate. In unit-aware applications, a file parameter value may also include an explicit unit, for example Mw=1131 Da;T=25 ºC;gdot=0.1 1/s;.

  • Then the data columns should appear, separated by spaces or tabs.

  • In unit-aware applications, column headers may include units in square brackets or parentheses, for example t [min] or G' [kPa]. See Units for the supported units and current limitations.

.laos extension

Text files with .laos extension should be organised as follows:

  • .laos files should contaion at least the parameter values for the:

    1. Frequency omega,

    2. Amplitude gamma.

  • 3 columns separated by spaces or tabs containing respectively:

    1. time, \(t\),

    2. strain, \(\gamma\),

    3. stress \(\sigma\).

Other columns will be ignored. The top of a correct .laos file looks like:

omega=0.3;gamma=3.16;
#time   Strain(-)       Stress(Pa)
0.082   0.07802         8.5946
0.445   0.42041         10.804
0.814   0.7637          11.736
1.187   1.1018          11.959
1.559   1.4245          11.807
1.924   1.7241          11.419
2.292   2.0053          10.893
2.659   2.262           10.246
...     ...         ...

Views

sigma,gamma(t) displays the raw stress and raw strain as functions of time. Use it as a first check that the loaded signal has the expected oscillatory shape. sigma SCA,gamma(t) shows the same raw strain together with the raw stress scaled by its maximum absolute value, which is useful when comparing the phase of stress and strain on the same plot. sigma(t) and gamma(t) show the raw stress or raw strain separately.

sigma(gamma) plots the raw stress against the raw strain. This is the direct stress-strain Lissajous curve from the imported data. sigma(gamma) FILT uses the Fourier reconstruction of the signal before plotting stress against strain.

FFT spectrum plots the normalized magnitude of the stress harmonics as a function of angular frequency. The spectrum is normalized by the fundamental harmonic and is shown on a logarithmic vertical axis. To keep the plot readable, the view displays at most the first 25 harmonics.

sigma(gdot) FILT plots the reconstructed stress against the reconstructed strain-rate. The strain-rate is calculated from the reconstructed strain and the file parameter omega.

sigma(gamma) ANLS and sigma(gdot) ANLS compare the filtered stress with elastic or viscous contributions reconstructed from selected odd harmonics. They also include the contribution reconstructed from the first and third harmonics.

Cheb elastic and Cheb viscous display the elastic and viscous Chebyshev coefficients obtained from the Fourier coefficients of the stress signal. These views are intended for harmonic analysis after checking that the raw signal is suitable for Fourier processing.

The filtered, FFT, analysis, and Chebyshev views show two additional controls in the view toolbar. HHSR is the highest harmonic considered in the stress reconstruction. PPQC is the number of points per quarter cycle used in the Fourier reconstruction; it can be set between 20 and 500.

The Fourier-based views interpolate the signal onto an evenly spaced time grid and identify cycles from zero crossings of the strain signal. They are therefore most appropriate for periodic LAOS data with a clear oscillatory strain signal.