Decomposition of deformation into bend, stretch and twist?

Question

I'm wondering is there any way to decompose the deformation of an object into different components? For example, into stretching, bending and twisting part respectively? The decomposition could be applied to any description of deformation, either to deformation gradient tensor, strain tensor or stress tensor.

To my knowledge, there is some literature using the decomposition of deformation gradient tensor into rotation and deformation part. But what I want is to further decompose the deformation, leave away the rigid transformation like translating and rotating.

Thanks!

Answer 1

There is no unique way to "further decompose" the deformation into the "rigid transformation" and "others" because whatever "rigid part" you choose, you may always calculate "others" as a simple difference (that's because there's really no global constraint on the "other" part). So the "rigid part" may be anything you want.