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Neo-Hookean solid - Uni-axial extension | | Neo-Hookean solid - Uni-axial extension: Encyclopedia II - Neo-Hookean solid - Uni-axial extension | | Under uni-axial extension from the definition of Finger tensor:
where where α - is the elongation (ratio of deformed and undeformed length of the sample)
Assuming no traction on the sides T22 = T33 = 0, so:
,
where ε = α1 − 1 is the strain.
The equation above is for the true stress (ratio of the elongation force to defor ...
See also:Neo-Hookean solid, Neo-Hookean solid - Uni-axial extension, Neo-Hookean solid - Simple shear, Neo-Hookean solid - Generalization, Neo-Hookean solid - Source | | | Neo-Hookean solid, Neo-Hookean solid - Generalization, Neo-Hookean solid - Simple shear, Neo-Hookean solid - Source, Neo-Hookean solid - Uni-axial extension | | |
| | | Neo-Hookean solid: Encyclopedia II - Neo-Hookean solid - Uni-axial extension
Neo-Hookean solid - Uni-axial extension
Under uni-axial extension from the definition of Finger tensor:
where where α - is the elongation (ratio of deformed and undeformed length of the sample)
Assuming no traction on the sides T22 = T33 = 0, so:
,
where ε = α1 − 1 is the strain.
The equation above is for the true stress (ratio of the elongation force to deformed cross-section), for engineering stress the equation is:
T11eng = G(α1 − α − 2)
For small deformations ε < < 0 we will have:
T11 = 3Gε
Thus, the Young's modulus of a neo-Hookean solid is 3G.
Other related archives1948, Cleanup from November 2005, Continuum mechanics, Finger tensor, Hooke's law, Mooney-Rivlin solid, Non-Newtonian fluids, Pages needing expert attention, Ronald Rivlin, Young's modulus, deformations, energy, engineering stress, first invariant, incompressible media, plastics, pressure, rubber, shear modulus, simple shear, strain, stress, tensor, trace
 Adapted from the Wikipedia article "Uni-axial extension", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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