How to calculate shear strain under ensemble analysis for every frame

[Sakshi]

I have total 2498 set of images  of contracting gel and I want to calculate strain via PIV for every frame as the gel contracting with time. But with the ensemble analysis setting, only one frame is analyzed. Is there any way to analyze all frames?

[William Thielicke]

Hi, the idea of ensemble analysis is to use all images to get one single vector map. If you need a time resolved analysis, then  ensemble correlation is not a suitable method.

[Sakshi]

Thank you so much. So, what would you suggest to calculate the strain?

[William Thielicke]

Visakh might be able to help:

https://groups.google.com/g/pivlab/c/IrxZq0Pge0o

[Visakh M G]

Thank you William.

I will re-quote my previous discussion with William.

As per my understanding, and based on the references (kindly refer to section 3.4 in Fluid Mechanics by Cohen  and Kundu 5th edition or section 2.4 of Viscous Fluid Flow by Papanastasiou or even Wikipedia https://en.wikipedia.org/wiki/Strain-rate_tensor), the strain rate tensor is defined as S = 1/2 (∇u + ∇u^T).

 If you have the velocity field data, you may calculate the Strain rate tensor as per the above formula. It is a symmetric tensor, the off-diagonal elements are same for 2D case, and is equal to 1/2(∂v/∂x + ∂u/∂y) which is the shear strain.

The trace (sum of the diagonal elements) is the bulk /volumetric strain rate ∇.u = ∂u/∂x + ∂v/∂y for 2D case and is equal to the divergence of the velocity field, which is also the first invariant of the strain rate tensor. The diagonal components of the strain rate tensor are the linear strain rates i.e, for x-direction ∂u/∂x and for y-direction, ∂v/∂y separately. Their sum for 2D flows is the volumetric strain rate for compressible flows and is 0 for 2D incompressible flows. For 3D incompressible flows, this sum is -∂w/∂z.

Regards,

Visakh

[Sakshi]

Thank you so much.

Are the strain and shear rates incorporated in the PIVlab the same as you mentioned above? 

[Visakh M G]

Not exactly. The simple shear in PIVLab (which is actually the shear strain rate = ∂v/∂x + ∂u/∂y) is consistent as per the literature. However, the simple strain in PIVLab is defined as ∂u/∂x - ∂v/∂y, for which I couldn't find any meaning, or in any textbooks on fluid mechanics. After discussion with William, I have opened an issue on GitHub.

https://groups.google.com/g/pivlab/c/IrxZq0Pge0o