Difference between revisions of "Comparison of Neo-Hookean Materials"
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<li>[[Mooney Material]]<br> | <li>[[Mooney Material]]<br> | ||
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<math>W = | <math>W = {\lambda\over 2}(J_E-1)^2 + G\sum_k (\lambda_k-1)^2</math> | ||
</li> | </li> | ||
Revision as of 14:40, 16 November 2017
Introduction
The definition of an isotropic, neo-Hookean is an elastic material that depends ot two elastic constants and in the limit of small deformations is identical to a small-strain, linear-elastic, Hookean material. The currently available MPM Materials that a neo-Hookean material options are:
The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G1 and G2). Is can be considered as neo-Hooken that reduce to small strain material with same bulk modulus and shear modulus G = G1+ G2. The third allows plastic deformation by limiting the amount of elongation in tension or compressure. By turning off the clamping, the clamped neo-Hookean material represents a modified corotated elasticity law.
Elastic Energy Functions
The elastic energy functions for these three material compared are:
- Neo-Hookean Material
[math]\displaystyle{ W =U(J) + {G\over 2 } (I_{1}-3-2\ln J) }[/math] - Mooney Material
[math]\displaystyle{ W =U(J) + {G_{1} \over 2 } (\bar I_{1}-3) + {G_{2} \over 2 }(\bar I_{2}-3) }[/math] - Mooney Material
[math]\displaystyle{ W = {\lambda\over 2}(J_E-1)^2 + G\sum_k (\lambda_k-1)^2 }[/math]