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Why can gases and liquids change volume under pressure but not support shear stress?

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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 the mechanics of solids, fluids—which include both liquids and gases—are defined by their inability to sustain shear stress when at rest.12

Why Fluids Cannot Support Shear Stress

A material is considered a solid if it can support a substantial shearing force, which allows it to maintain a definite shape. In contrast, fluids lack an enduring atomic-scale structure. Because the atoms or molecules in a fluid are mobile and continually wander throughout the material, they cannot maintain a fixed position relative to one another. When a shear stress is applied, these layers of fluid move over each other, resulting in continuous, irrecoverable deformation known as flow.3214

Volume Changes Under Pressure

While fluids cannot support shear stress, they can support normal stress, which acts perpendicular to a material plane. When forces are applied perpendicularly to all surfaces of a fluid, this is known as hydrostatic pressure. Under such pressure, fluids can undergo changes in volume; gases are highly compressible, while liquids are generally much less compressible but still exhibit volume changes under sufficient pressure.3145