Neo-Hookean material

It involves only two elastic constants. A special case, where fc = 0, is the neo-Hookean material, which can be derived from thermodynamics principles for a simple solid. Exact solutions can be obtained for the cylindrical deformation of a thick-walled tube. In the case where there is no residual strain, we have... 

Minimization of the total elastic strain energy suggests that the rod will become unstable at a critical amount of torsion part of the rod will unwind and form a tight ring while the remainder of the rod will become slightly more stretched. A simple criterion can be derived on this basis for the onset of kinks. For a neo-Hookean material, Eq. (1.8), the condition for forming a kink becomes ... 

For the Neo-Hookean material, the strain energy density function is the same as the Mooney-Rivlin material but with C2 = 0 ... 

Neo-Hookean material This is an extension of the linear elastic Hooke s law to include large deformations. The main difference between the classical Hooke s law and the Neo-Hookean law is that in the latter the shear modulus is a function of the deformations. The strain energy density for the compressible Neo-Hookean model is given by... 

The voltage-charge diagram represents fire equilibrium pafli in terms of electrical quantities. For the neo-Hookean material the law can be written analytically as... 

The strain energy density function V for a compressible isotropic neo-Hookean material (see Attard Hunt (2004)) is given by ... 

One would be in an ad-hoc fashion to assume that, because of the tendency toward interpenetration, near the crack tips the crack surfaces would come in smooth contact and form a cusp, and the resulting contact region would consist of a single uninterrupted zone rather than the sum of a series of discrete zones as implied by the oscillatory nature of the elastic solution (see Comninou [ll], Atkinson [l2]). Another way is to assume that near the crack tip the linear theory is not valid and to use a large deformation nonlinear theory. An asymptotic analysis using such a theory was provided by Knowles and Sternberg [l3] for the plane stress interface crack problem in two bonded dissimilar incompressible Neo-Hookean materials which shows no oscillatory behavior for stresses or... 

VI. An Estimate of the Internal Energy for a Compressible Neo-Hookean Material in Simple Tension... 

As the stretch increases, U increases monotonically with the stretch for a compressible neo-Hookean material. The rate at which it increases depends on the important parameter (m-1) which measures departure from ideality. According to data presented previously by Shen and Blatz the best current value for m... 

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