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Why do water and air fail to provide long-term support for 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).

In the context of physics, water and air are classified as fluids, which are defined by their inability to sustain a tangential or shear stress when at rest.1

Unlike elastic solids, which can maintain internal shearing forces when twisted or flexed and return to their original shape once the force is removed, fluids yield to shear stress regardless of how small that stress may be. When subjected to such stress, fluids undergo a continuous and irrecoverable change in shape, a process known as flow.123

This behavior occurs because, in fluids, adjacent layers move over one another at different velocities. The resistance to this motion is determined by the fluid's viscosity, which acts as a form of internal friction. Because fluids cannot resist these tangential forces, they cannot maintain a static shape under shear; instead, they continuously deform until the applied stress is removed or the fluid reaches a new equilibrium.312