A displacement field shows the change in position points before and after deformation in a group of displacement vectors. The displacement field does not, however, show how the particles moved during deformation history, but links the undeformed and deformed states. Particle paths show the motion of those points during deformation.
Rotation indicates rigid rotation of the entire deformed rock body. It involves uniform rotation of the rock volume relative to an external coordinate system. Large-scale rotations occur in thrust nappes or tectonic plates, usually around vertical axes. Fault blocks may rotate around horizontal axes in extensional settings.
Translation is where every particle in the rock body moves in the same direction, over the same distance. Displacement fields consist of parallel vectors of equal length. Translation of nappes can occur over 10s or 100s km.
Shear strain describes the strain due to rotation about an axis. It is deformation which involves change in internal shape.
Simple shear is a special type of constant-volume plane strain deformation. No stretching or shortening of lines or movement in the third direction of particles occurs. It is non-coaxial deformation, meaning that lines parallel to the principal strain axes have rotated away from their initial positions.
Subsimple shear is a spectrum of planar deformations between pure shear and simple shear. Internal rotation is less than for simple shear.
Pure shear is a perfect coaxial deformation. Particles parallel to the principal axes do not rotate from their initial positions. Pure shear is a plane strain with no volume change associated.
Rigid body deformation (rotation & translation),
and shear strain (simple, subsimple, & pure shear).
From Haakon Fossen's Structural Geology (2010).
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