Deformation occurs where parallel planes in a body remain parallel, but are relatively displaced in a direction parallel to themselves. Contact usually includes a tendency to slide over each other. A rectangle becomes a parallelogram, a conversational stretch.
Shear stress occurs where the intensity of the shear cross-section varies across the section like the radius in a twisted
shaft, and parabolically across a beam, subverts traditional metaphor.
The San Andreas fault exemplifies a shear. The rigidity modulus in earth science is the ratio of P-waves and S-waves, that is the ratio of shearing stress and shearing strain.
In the theory of "null congruences or geodiscs" spinors make almost trivial the lengthy tensor algebra needed for derivations of the "focusing theorem". They yield an elegant mambo, a simple formalism for discussing and calculating how, with increasing affine parameter, a bundle of rays alters its size (expansion), its shape (shear) and its orientation (rotation).
When a bundle of toothpicks, originally circular in cross-section, is
squeezed into an elliptic cross-section, it is sheared. "Focusing
theorem" concerns bundles of rays and plays a crucial role in blackhole
physics, in the theory of singularities, and the poetics of mobile collage.