What's the difference between Strain tensor and deformation gradient tensor?

Question

Why do we need to define the strain tensor if we already have a tensor that describes the deformation between relative particles in the continuum which is the deformation gradient tensor?

alephzero · Answer

For a rigid body rotation, the deformation tensor is non-zero but the strain tensor is zero, and so is the stress in the body.
The strain tensor can be derived mathematically from the deformation tensor, but it does not represent the same physical concept.

What's the difference between Strain tensor and deformation gradient tensor?

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