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How does twisting a metal bar create shear stress?

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Figure 1: The position vector x and the velocity vector v of a material point, the body force fdV acting on an element dV of volume, and the surface force TdS acting on an element dS of surface in a Cartesian coordinate system 1, 2, 3 (see text).
mechanics of solids Figure 1: The position vector x and the velocity vector v of a material point, the body force fdV acting on an element dV of volume, and the surface force TdS acting on an element dS of surface in a Cartesian coordinate system 1, 2, 3 (see text).

When a metal bar is twisted about its longitudinal axis, it experiences shear stress because the applied force acts parallel to the cross-sectional planes of the material.1

In the context of mechanics of solids, this twisting action—known as torsion—causes the internal particles of the metal to displace from their original positions. Specifically, the force creates shear strain, where the internal right angles of the material are deformed into acute or obtuse angles as the cross-sections shift relative to one another.1

Essentially, the twisting motion forces the material to undergo deformation by slippage along these parallel planes. While a torsion bar is designed to resist this twisting and return to its original shape, the internal resistance to this deformation is what manifests as shear stress throughout the bar.231