Elasticity (physics) in the context of Crystal structure

Pierre Maurice Marie Duhem (French: [pjɛʁ mɔʁis maʁi dy.ɛm, moʁ-] ; 9 June 1861 – 14 September 1916) was a French theoretical physicist who made significant contributions to thermodynamics, hydrodynamics, and the theory of elasticity. Duhem was also a prolific historian of science, noted especially for his pioneering work on the European Middle Ages. As a philosopher of science, Duhem is credited with the "Duhem–Quine thesis" on the indeterminacy of experimental criteria. Duhem's opposition to positivism was partly informed by his traditionalist Catholicism, an outlook that put him at odds with the dominant academic currents in France during his lifetime.

In physics, a force is an action (usually a push or a pull) that can cause an object to change its velocity or its shape, or to resist other forces, or to cause changes of pressure in a fluid. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity (force vector). The SI unit of force is the newton (N), and force is often represented by the symbol F.

Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion. Types of forces often encountered in classical mechanics include elastic, frictional, contact or "normal" forces, and gravitational. The rotational version of force is torque, which produces changes in the rotational speed of an object. In an extended body, each part applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress. In the case of multiple forces, if the net force on an extended body is zero the body is in equilibrium.

The bow and arrow is a ranged weapon system consisting of an elastic launching device (bow) and long-shafted projectiles (arrows). Humans used bows and arrows for hunting and aggression long before recorded history, and the practice was common to many prehistoric cultures. They were important weapons of war from ancient history until the early modern period, when they were rendered increasingly obsolete by the development of the more powerful and accurate firearms. Today, bows and arrows are mostly used for hunting and sports.

Archery is the art, practice, or skill of using bows to shoot arrows. A person who shoots arrows with a bow is called a bowman or an archer. Someone who makes bows is known as a bowyer, someone who makes arrows is a fletcher, and someone who manufactures metal arrowheads is an arrowsmith.

In physics and materials science, plasticity (also known as plastic deformation) is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.

Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams. However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can result. In brittle materials such as rock, concrete and bone, plasticity is caused predominantly by slip at microcracks. In cellular materials such as liquid foams or biological tissues, plasticity is mainly a consequence of bubble or cell rearrangements, notably T1 processes.

Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into other forms of energy, such as kinetic energy and sound energy, when the object is allowed to return to its original shape (reformation) by its elasticity.

$${\displaystyle U={\frac {1}{2}}k\,\Delta x^{2}}$$

A seismic wave is a mechanical wave of acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake (or generally, a quake), volcanic eruption, magma movement, a large landslide and a large man-made explosion that produces low-frequency acoustic energy. Seismic waves are studied by seismologists, who record the waves using seismometers, hydrophones (in water), or accelerometers. Seismic waves are distinguished from seismic noise (ambient vibration), which is persistent low-amplitude vibration arising from a variety of natural and anthropogenic sources.

The propagation velocity of a seismic wave depends on density and elasticity of the medium as well as the type of wave. Velocity tends to increase with depth through Earth's crust and mantle, but drops sharply going from the mantle to Earth's outer core.

A crossbow is a ranged weapon using an elastic launching device consisting of a bow-like assembly called a prod, mounted horizontally on a main frame called a tiller, which is hand-held in a similar fashion to the stock of a long gun. Crossbows shoot arrow-like projectiles called bolts or quarrels. A person who shoots crossbow is called a crossbowman, an arbalister or an arbalist (after the arbalest, a European crossbow variant used during the 12th century).

Crossbows and bows use the same elastic launch principles, but differ in that an archer using a bow must draw-and-shoot in a quick and smooth motion with limited or no time for aiming, while a crossbow's design allows it to be spanned and cocked ready for use at a later time and thus affording the wielder unlimited time to aim. When shooting a bow, the archer must first fully perform the draw, holding the string and arrow while pulling them back with arm and back muscles, and then either immediately loose without a period of aiming, or hold that form while aiming. When using the heavy bows suitable for warfare, both actions demand some physical strength. As such, the accurate and sustained use of a bow in warfare takes much practice.

In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.

The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. For most metals, such as aluminium and cold-worked steel, there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield point (or proof stress) is taken as the stress at which 0.2% plastic deformation occurs. Yielding is a gradual failure mode which is normally not catastrophic, unlike ultimate failure.

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.

In solid mechanics, the shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:

A torsion spring is a spring that works by twisting its end along its axis; that is, a flexible elastic object that stores mechanical energy when it is twisted. When it is twisted, it exerts a torque in the opposite direction, proportional to the amount (angle) it is twisted. There are various types:

• A torsion bar is a straight bar of metal or rubber that is subjected to twisting (shear stress) about its axis by torque applied at its ends.
• A more delicate form used in sensitive instruments, called a torsion fiber consists of a fiber of silk, glass, or quartz under tension, that is twisted about its axis.
• A helical torsion spring, is a metal rod or wire in the shape of a helix (coil) that is subjected to twisting about the axis of the coil by sideways forces (bending moments) applied to its ends, twisting the coil tighter.
• Clocks use a spiral wound torsion spring (a form of helical torsion spring where the coils are around each other instead of piled up) sometimes called a "clock spring" or colloquially called a mainspring. Those types of torsion springs are also used for attic stairs, clutches, typewriters and other devices that need near constant torque for large angles or even multiple revolutions.

Rubber elasticity is the ability of solid rubber to be stretched up to a factor of 10 from its original length, and return to close to its original length upon release. This process can be repeated many times with no apparent degradation to the rubber.

Rubber, like all materials, consists of molecules. Rubber's elasticity is produced by molecular processes that occur due to its molecular structure. Rubber's molecules are polymers, or large, chain-like molecules. Polymers are produced by a process called polymerization. This process builds polymers up by sequentially adding short molecular backbone units to the chain through chemical reactions. A rubber polymer follows a random winding path in three dimensions, intermingling with many other rubber polymers.

An elastomer is a polymer with viscoelasticity (i.e. both viscosity and elasticity) and with weak intermolecular forces, generally low Young's modulus (E) and high failure strain compared with other materials. The term, a portmanteau of elastic polymer, is often used interchangeably with rubber, although the latter is preferred when referring to vulcanisates. Each of the monomers which link to form the polymer is usually a compound of several elements among carbon, hydrogen, oxygen and silicon. Elastomers are amorphous polymers maintained above their glass transition temperature, so that considerable molecular reconformation is feasible without breaking of covalent bonds.

Rubber-like solids with elastic properties are called elastomers. Polymer chains are held together in these materials by relatively weak intermolecular bonds, which permit the polymers to stretch in response to macroscopic stresses.

In physics, a mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a material medium. Vacuum is, from classical perspective, a non-material medium, where electromagnetic waves propagate.

While waves can move over long distances, the movement of the medium of transmission—the material—is limited. Therefore, the oscillating material does not move far from its initial equilibrium position. Mechanical waves can be produced only in media which possess elasticity and inertia. There are three types of mechanical waves: transverse waves, longitudinal waves, and surface waves. Some of the most common examples of mechanical waves are water waves, sound waves, and seismic waves.

Longitudinal waves are waves which oscillate in the direction which is parallel to the direction in which the wave travels and displacement of the medium is in the same (or opposite) direction of the wave propagation. Mechanical longitudinal waves are also called compressional or compression waves, because they produce compression and rarefaction when travelling through a medium, and pressure waves, because they produce increases and decreases in pressure. A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an elastic medium) and seismic P waves (created by earthquakes and explosions).

The other main type of wave is the transverse wave, in which the displacements of the medium are at right angles to the direction of propagation. Transverse waves, for instance, describe some bulk sound waves in solid materials (but not in fluids); these are also called "shear waves" to differentiate them from the (longitudinal) pressure waves that these materials also support.