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In this video at 6:15 https://www.youtube.com/watch?v=ZO8P2iiQGDc

By calculation, it is clear that displacement gradient tensor equal to zero when the motion is pure shifting (no change in shape).

But intuitively, it is not since the displacement by definition is the relative position of a particle in its current configuration with respect to its position in the initial configuration.

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When the system evolves over time, the coordinate axis also changes its position. The first diagram tracks local axis in shifting motion. Displacement is the relative distance between two global coordinates. Deformation is the shift in local coordinates.

Tracking Local Axis in Shifting Motion

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