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NeoHookean solidNeoHookean solid model is an extension of Hooke's law for the case of large deformations. The model of neoHookean solid is usable for plastics and rubberlike substances. The response of a neoHookean material, or hyperelastic material, to an applied stress differs from that of a linear elastic material. While a linear elastic material has a linear relationship between applied stress and strain, a neoHookean material does not. A hyperelastic material will initially be linear, but at a certain point, the stressstrain curve will plateau due to the release of energy as heat while straining the material. Then, at another point, the elastic modulus of the material will increase again. This hyperelasticity, or rubber elasticity, is often observed in polymers. Crosslinked polymers will act in this way because initially the polymer chains can move relative to each other when a stress is applied. However, at a certain point the polymer chains will be stretched to the maximum point that the covalent cross links will allow, and this will cause a dramatic increase in the elastic modulus of the material. One can also use thermodynamics to explain the elasticity of polymers. Additional recommended knowledge
NeoHookean Solid ModelThe model of neoHookean solid assumes that the extra stresses due to deformation are proportional to Finger tensor:
where  stress tensor, p  pressure,  is the unity tensor, G is a constant equal to shear modulus, is the Finger tensor. The strain energy for this model is:
where W is potential energy and is the trace (or first invariant) of Finger tensor . Usually the model is used for incompressible media. The model was proposed by Ronald Rivlin in 1948. Uniaxial extension
Under uniaxial extension from the definition of Finger tensor: where α_{1} is the elongation in the stretch ratio in the 1direction. Assuming no traction on the sides, T_{22} = T_{33} = 0, so:
where ε = α_{1} − 1 is the strain. The equation above is for the true stress (ratio of the elongation force to deformed crosssection), for engineering stress the equation is: For small deformations ε < < 1 we will have:
Thus, the equivalent Young's modulus of a neoHookean solid in uniaxial extension is 3G. Simple shearFor the case of simple shear we will have:
where γ is shear deformation. Thus neoHookean solid shows linear dependence of shear stresses upon shear deformation and quadratic first difference of normal stresses. GeneralizationThe most important generalisation of NeoHookean solid is MooneyRivlin solid. Source
Categories: Continuum mechanics  NonNewtonian fluids  Rubber properties 

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "NeoHookean_solid". A list of authors is available in Wikipedia. 