Toward fully anisotropic viscoelastic material models using an automated high-speed optical rig

This paper describes some of the algorithms that are employed in the postprocessing of the data obtained from an automated high-speed optical rig. The setup, entirely designed by some of the authors, is used for measuring the full field displacement in time of anisotropic viscoelastic solids undergoing controlled dynamic excitation. The setup main goal is to provide complex transfer functions relating the three-dimensional sinusoidal displacement on the surface of the sample to the sinusoidal motion of the foundation, suitable for the inverse estimation of the dynamic properties of the material under analysis. The complete automation of the measurement process aims at maximizing repeatability and signal-to-noise ratio. In particular, a stereo high-speed camera system is responsible for the actual measurement, while a laser Doppler vibrometer is used for a preliminary autoranging procedure and for data validation.

The camera system does not directly output the high-quality data that is needed for a successful, physically meaningful inverse estimation. Hence, here the algorithms described in this paper come into play. Since digital image correlation (DIC) may fail in some frames or in some regions of the pictures, a mask is applied and calculated for every measurement run to preserve information only where the success rate of the DIC algorithm is higher than a specified threshold. The sample is mounted on a foundation whose sides are flat: random sample consensus (RANSAC) and principal component analysis (PCA) are used to respectively eliminate outliers and find the best fitting plane to the foundation side – the measured displacement field can then be expressed in a local coordinate system, truly relative to the foundation. The transfer functions are now obtained in two steps: first an optimizer is used to fit a cosine to all the measured displacement time-series, then the complex amplitudes representing the motion of the sample faces are divided by the average of the complex amplitudes representing the motion of the foundation. (paper)