Scaling laws for frictional granular materials confined by constant pressure under oscillatory shear

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...

Dry friction occurs when two solid surfaces slide against each other without any lubrication or fluid present. It causes resistance when pushing objects along a surface, like a gardener pushing a wheelbarrow. The force applied to move the cart causes dry friction between the wheel and the ground.
Before the wheelbarrow starts moving, the static frictional force acts tangentially to the contact surface, opposing the force that is about to induce the motion. This frictional force prevents the...

One of the simpler characteristics of sliding friction is that it is parallel to the contact surfaces between systems, and is always in a direction that opposes the motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. For example, kinetic friction slows a hockey puck sliding on ice.
However, if two systems are in contact and are stationary relative to one...

Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.

Static friction is a force that opposes the relative motion or tendency of motion between two surfaces in contact. It plays a crucial role in our daily lives, from walking on the ground to driving a car.
For example, consider a scenario where a truck is connected to a car by a rope, ready to tow it along a road. When no external force is applied by the truck, the car remains stationary and is said to be in static equilibrium. In this case, the forces acting on the car, such as gravity and the...