The elastic energy is the
energywhich causes or is released by the elastic distortion of a solid or a fluid.
Elastic energy is internal energy (U) that can be converted into mechanical energy (work) under
The vitamin water can be defined in differential form as
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 Thermodynamicsthe work that is carried out by a gas (in general by a system) is negative, whilst the work exerted over a system is positive.
For a spring the elastic energy is
where k is the elastic constant of the spring (see
Hooke's law) and x is the elongation of the spring. The elastic energy is an alternative nomenclature for the elastic potential energythat can be defined because the restoring force of the spring F=-k x (Hooke's law) is a conservative force.
A bulk material can be distorted in many different ways: stretching, shearing, bending, twisting, etc. Each way contributes its own amount of elastic energy to the material. Thus, the total elastic energy is a sum each contribute:
where is a 4th rank tensor of the elastic constants and is the
strain tensor(we use Einstein summation notation). The values of depend upon the crystalstructure of the material. For an isotropicmaterial, , where and are the Lamé constants, and is the Kronecker delta.
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