I have small-scale prisms DIC's data and I am wondering about removing the rigid body motion from all the data or just until the peak load(elastic stage).
Dear Helmi Alguhi
The literature that may be useful are.
https://hal.archives-ouvertes.fr/file/index/docid/1025172/filename/Passieux_ExpMech14_spheres.pdf
Article Uncertainty Quantification for DIC Displacement Measurements...
https://inis.iaea.org/collection/NCLCollectionStore/_Public/43/070/43070819.pdf
The answer depends on the quantities, which you want to measure. If you want deformation, then you only need to eliminate rigid body rotation. In small deformations, you have strain εij=1/2(𝜕ui/𝜕uj+𝜕uj/𝜕ui)=εji , which excludes rigid body motions. The rigid body rotation is ωij=1/2(𝜕ui/𝜕uj--𝜕uj/𝜕ui)=--ωji.
In large deformations and large displacements, you have the deformation gradient FiJ=𝜕xi/𝜕XJ, which includes rigid rotations. Then you need to consider left or right polar decomposition. You may exclude rigid body rotation by using one of the stretch tensors or one of the Cauchy-Green tensors, see https://en.wikipedia.org/wiki/Finite_strain_theory
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