Everything about Elasticity Physics totally explained
Elasticity is a branch of physics which studies the properties of
elastic materials. A material is said to be elastic if it
deforms under
stress (for example, external
forces), but then returns to its original shape when the stress is removed. The amount of deformation is called the
strain.
Modeling elasticity
The elastic regime is characterized by a linear relationship between stress and strain, denoted
linear elasticity. Good examples are a rubber band and a bouncing ball. This idea was first stated by
Robert Hooke in 1675 as a Latin anagram "ceiiinosssttuv", whose solution he published in 1678 as "
Ut tensio, sic vis" which means "
As the extension, so the force."
This linear relationship is called
Hooke's law. The classic model of linear elasticity is the perfect
spring. Although the general proportionality constant between stress and strain in three dimensions is a 4th order
tensor, when considering simple situations of higher
symmetry such as a rod in one dimensional loading, the relationship may often be reduced to applications of Hooke's law.
Because most materials are elastic only under relatively small deformations, several assumptions are used to linearize the theory. Most importantly, higher order terms are generally discarded based on the small deformation assumption. In certain special cases, such as when considering a rubbery material, these assumptions may not be permissible. However, in general, elasticity refers to the linearized theory of the continuum stresses and strains.
Transitions to inelasticity
Above a certain stress known as the
elastic limit or the
yield strength of an elastic material, the relationship between stress and strain becomes nonlinear. Beyond this limit, the
solid may deform irreversibly, exhibiting
plasticity. A
stress-strain curve is one tool for visualizing this transition.
Furthermore, not only solids exhibit elasticity. Some
non-Newtonian fluids, such as
viscoelastic fluids, will also exhibit elasticity in certain conditions. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow, exhibiting
viscosity.
Further Information
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