Spatial correlations in sheared isothermal liquids: from elastic particles to granular particles

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...

Most solids and liquids are incompressible—their densities remain constant throughout. In the presence of an external force, the molecules tend to restore to their original positions, which is only possible because the constituents interact. The interactions help the constituents pass on information about external disturbances, like sound waves. Therefore, sound waves travel faster through these media. Compared to solids, the constituents in a liquid are less tightly bound. Thus, sound waves...

When a force is applied parallel to the top surface of a solid, it resists the applied force due to the internal frictional forces between the layers of the solid known as shearing resistance. However, when the force is removed, the shearing forces restore the original shape of the solid. Other deformation forces also cause temporary changes in shape if the forces are not beyond a threshold magnitude. Solids tend to retain their shape, making the study of their rest and motion easier. Beyond...

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...