Shear modulus in the context of Elasticity (physics)

In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (flow) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

Although the term fluid generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of solid vary as well, and depending on field, some substances can have both fluid and solid properties. Non-Newtonian fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers to any liquid constituent of the body (body fluid), whereas "liquid" is not used in this sense. Sometimes liquids given for fluid replacement, either by drinking or by injection, are also called fluids (e.g. "drink plenty of fluids"). In hydraulics, fluid is a term which refers to liquids with certain properties, and is broader than (hydraulic) oils.

Crystal growth is a major stage of a crystallization process, and consists of the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. The growth typically follows an initial stage of either homogeneous or heterogeneous (surface catalyzed) nucleation, unless a "seed" crystal, purposely added to start the growth, was already present.

The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other.The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation (i.e. changes of shape and/or volume). Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically exhibit the capacity for macroscopic viscous flow.

The bulk modulus (${\displaystyle K}$ or ${\displaystyle B}$ or ${\displaystyle k}$) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility.

A coil spring is a mechanical device that typically is used to store energy and subsequently release it, to absorb shock, or to maintain a force between contacting surfaces. It is made of an elastic material formed into the shape of a helix that returns to its natural length when unloaded.

Under tension or compression, the material (wire) of a coil spring undergoes torsion. The spring characteristics therefore depend on the shear modulus.

Seismic moment is a quantity used by seismologists to measure the size of an earthquake. The scalar seismic moment ${\displaystyle M_{0}}$ is defined by the equation${\displaystyle M_{0}=\mu AD}$, where

• ${\displaystyle \mu }$ is the shear modulus of the rocks involved in the earthquake (in pascals (Pa), i.e. newtons per square meter)
• ${\displaystyle A}$ is the area of the rupture along the geologic fault where the earthquake occurred (in square meters), and
• ${\displaystyle D}$ is the average slip (displacement offset between the two sides of the fault) on ${\displaystyle A}$ (in meters).

${\displaystyle M_{0}}$ thus has dimensions of torque, measured in newton meters. The connection between seismic moment and a torque is natural in the body-force equivalent representation of seismic sources as a double-couple (a pair of force couples with opposite torques): the seismic moment is the torque of each of the two couples. Despite having the same dimensions as energy, seismic moment is not a measure of energy. The relations between seismic moment, potential energy drop and radiated energy are indirect and approximative.