In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence or stress and to return to its original size and shape when the stress is removed. Solid objects will deform when forces are applied on them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.
The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied.
Perfect elasticity is an approximation of the real world, and few materials remain purely elastic even after very small deformations. In engineering, the amount of elasticity of a material is determined by two types of material parameter. The first type of material parameter is called a modulus, which measures the amount of force per unit area (stress) needed to achieve a given amount of deformation. The units of modulus are pascals (Pa) or pounds of force per square inch (psi, also lbf/in2). A higher modulus typically indicates that the material is harder to deform. The second type of parameter measures the elastic limit. The limit can be a stress beyond which the material no longer behaves elastic and deformation of the material will take place. If the stress is released, the material will elastically return to a permanent deformed shape instead of the original shape.
When describing the relative elasticities of two materials, both the modulus and the elastic limit have to be considered. Rubbers typically have a low modulus and tend to stretch a lot (that is, they have a high elastic limit) and so appear more elastic than metals (high modulus and low elastic limit) in everyday experience. Of two rubber materials with the same elastic limit, the one with a lower modulus will appear to be more elastic.
Linear elasticity
As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain. This relationship is known as Hooke's law. A geometry-dependent version of the idea[5] was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force",[6][7][8] a linear relationship commonly referred to as Hooke's law. This law can be stated as a relationship between force F and displacement x,
F= -kx
where k is a constant known as the rate or spring constant. It can also be stated as a relationship between stress σ and strain :
where E Is known as the elastic modulus or Young's modulus.
Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor, systems that exhibit symmetry, such as a one-dimensional rod, can often be reduced to applications of Hooke's law.
Finite elasticity[edit]The elastic behavior of objects that undergo finite deformations have been described using a number of models, such as Cauchy elastic material models, Hypoelastic materialmodels, and Hyperelastic material models. The primary measure that is used to quantity finite strains is the deformation gradient (F). More convenient strain measures can be derived from this primary quantity.
Viscosity
The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress.[1] For liquids, it corresponds to the informal concept of "thickness". For example, honey has a much higher viscosity than water.[2]
Viscosity is a property arising from collisions between neighboring particles in a fluid that are moving at different velocities. When the fluid is forced through a tube, the particles which comprise the fluid generally move more quickly near the tube's axis and more slowly near its walls: therefore some stress, (such as a pressure difference between the two ends of the tube), is needed to overcome the friction between particle layers to keep the fluid moving. For the same velocity pattern, the stress required is proportional to the fluid's viscosity.
A fluid that has no resistance to shear stress is known as an ideal or inviscid fluid. Zero viscosity is observed only at very low temperatures in superfluids. Otherwise, all fluids have positive viscosity, and are technically said to be viscous or viscid. In common parlance however, a liquid is said to be viscous if its viscosity is substantially greater than that of water; and may be described as mobile if the viscosity is noticeably less than water. A fluid with a relatively high viscosity, for example, pitch, may appear to be a solid.
Surface Tension
Surface tension is the elastic tendency of liquids which makes them acquire the least surface area possible. Surface tension is an important property that markedly influences many ecosystems. Surface tension is responsible, for example, when an object or insect (e.g.water striders) that is denser than water is able to float or run along the water surface.
At liquid-air interfaces, surface tension results from the greater attraction of water molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). The net effect is an inward force at its surface that causes water to behave as if its surface were covered with a stretched elastic membrane. Because of the relatively high attraction of water molecules for each other, water has a high surface tension (72.8 millinewtons per meter at 20 °C) compared to that of most other liquids. Surface tension is an important factor in the phenomenon of capillarity.
Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.
In materials science, surface tension is used for either surface stress or surface free energy.