Another way to look at strain

Here is another way to look at strain from PIV analysis of analogue models. After computing all the spatial derivatives of the velocity or incremental displacements field, the 2D small strain tensor can be assembled.

Below I calculated the principal strain direction from the small strain tensor. This is the direction of one of the principal strain, measured from the x-axis.

PrincipalSmallStrainsThetap

And then I calculated the values of the maximum principal strain and minimum principal strain. Two horizontal bands appear in the plot. The white cells in the top right and bottom left corners show that this experiment is a sinistral horizontal shear.

The data presented here is not interpolated. Each cell is a data point obtained from image cross-correlation. The maps could be interpolated and be made smoother.

PrincipalSmallStrainsEmax

PrincipalSmallStrainsEmin

and then we can claculate the maximum shear. We can see where the shear is occuring, where the difference between the maximum and minimum principal strains is largest.

PrincipalSmallStrainsGmax

Finally, since we have the directions and values of the principal small strains, we can plot them as crosses. The length of the line is linearly proportional to the magnitude of the principal strain, the orientation of the line is the orientation of the principal strain, and red indicates contraction while blue indicates extension.

PrincipalSmallStrainsCrossesCrop

A zoom-in shows the directions of S1 and S2 around the developping plastic shear zone fitting what we expect for a sinistral horizontal shear.

PrincipalSmallStrainsCrossesZoomCrop

I will integrate this into TecPIV rapidly.

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