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The elastic components, as previously mentioned, can be modeled as springs of elastic constant E, given the formula: = where σ is the stress, E is the elastic modulus of the material, and ε is the strain that occurs under the given stress, similar to Hooke's law.
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.
Proportionality limit Up to this amount of stress, stress is proportional to strain (Hooke's law), so the stress-strain graph is a straight line, and the gradient will be equal to the elastic modulus of the material. Elastic limit (yield strength) Beyond the elastic limit, permanent deformation will occur.
This is known as perfect elasticity, in which a given object will return to its original shape no matter how strongly it is deformed. This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs.
the ability of material to return to it's original shape after being stretched or compressed
The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure. [2] Upper limit theorem:
The persistence length equals the average projection of the end-to-end vector on the tangent to the chain contour at a chain end in the limit of infinite chain length. [ 4 ] The persistence length can be also expressed using the bending stiffness B s {\displaystyle B_{s}} , the Young's modulus E and knowing the section of the polymer chain.
A standard example of an entropic force is the elasticity of a freely jointed polymer molecule. [6] For an ideal chain, maximizing its entropy means reducing the distance between its two free ends. Consequently, a force that tends to collapse the chain is exerted by the ideal chain between its two free ends.