Elastic energy

The elastic energy is the energy which causes or is released by the elastic distortion of a solid or a fluid. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός A material is said to be elastic if it deforms under stress (e

Thermodynamics

Elastic energy is internal energy (U) that can be converted into mechanical energy (work) under adiabatic conditions.

The elastic energy can be defined in differential form as

$d U = d W = - P d V$

where P is the external pressure, equal to the internal pressure as the process is quasi-estatic (reversible), and V is the volume of the gas. The minus sign appears as the external pressure exerts a force contrary to the expansion. In Thermodynamics the work that is carried out by a gas (in general by a system) is negative, whilst the work exerted over a system is positive. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning "

Mechanics

For a spring the elastic energy is

$E = \frac{1}{2} k x^2$

where k is the elastic constant of the spring (see Hooke's law) and x is the elongation of the spring. A spring is a flexible elastic object used to store mechanical Energy. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the The elastic energy is an alternative nomenclature for the elastic potential energy that can be defined because the restoring force of the spring F=-k x (Hooke's law) is a conservative force. The elastic Potential energy is defined as a work (force x distance needed to compress or expand an elastic body

Continuum Systems

A bulk material can be distorted in many different ways: stretching, shearing, beading, twisting, etc. Each way contributes its own amount of elastic energy to the material. Thus, the total elastic energy is a sum each contribute:

$E = \frac12C_{ijkl}u_{ij}u_{lk}$ ,

where $C i j k l$ is a 4th rank tensor of the elastic constants and $u i j$ is the strain tensor (we use Einstein summation notation). History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually In Mathematics, especially in applications of Linear algebra to Physics, the Einstein notation or Einstein summation convention is a notational The values of $C i j k l$ depend upon the crystal structure of the material. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating For an isotropic material, $C i j k l = λδ i j δ k l + μ(δ i k δ j l + δ i l δ j k)$ , where $λ$ and $μ$ are the Lamé constants, and $δ i j$ is the Kronecker delta. Isotropy is uniformity in all directions Precise definitions depend on the subject area In Linear elasticity, the Lamé parameters are the two parameters λ also called Lamé's first parameter. In Mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker ( 1823 - 1891) is a function of two

Dictionary

-noun

(physics) The potential energy stored in a system when it is distorted or deformed; the classic example is that of a coiled spring

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