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This option is used to define the hyperelastic properties of a material. There are two optional parameters. The first one defines the model and can take one of the following strings: ARRUDA-BOYCE, MOONEY-RIVLIN, NEO HOOKE, OGDEN, POLYNOMIAL, REDUCED POLYNOMIAL or YEOH. The second parameter N makes sense for the OGDEN, POLYNOMIAL and REDUCED POLYMIAL model only, and determines the order of the strain energy potential. Default is the POLYNOMIAL model with N=1. All constants may be temperature dependent.
Let  ,
, and
 and  be defined by:
 be defined by:
|  |  |  | (341) | 
|  |  |  | (342) | 
|  |  |  | (343) | 
 ,
,  and
 and  are the invariants of the right Cauchy-Green deformation tensor
 are the invariants of the right Cauchy-Green deformation tensor 
 . The tensor
. The tensor  is linked to the Lagrange strain tensor
 is linked to the Lagrange strain tensor  by:
 by:
|  | (344) | 
 is the Kronecker symbol.
 is the Kronecker symbol. 
The Arruda-Boyce strain energy potential takes the form:
|  |  |  | |
|  |  | (345) | |
|  |  | 
The Mooney-Rivlin strain energy potential takes the form:
|  | (346) | 
 .
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The Neo-Hooke strain energy potential takes the form:
|  | (347) | 
 .
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The polynomial strain energy potential takes the form:
|  | (348) | 
 .
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The reduced polynomial strain energy potential takes the form:
|  | (349) | 
 . The reduced polynomial strain energy potential can be viewed as a special case of the polynomial strain energy potential
. The reduced polynomial strain energy potential can be viewed as a special case of the polynomial strain energy potential
The Yeoh strain energy potential is nothing else but the reduced polynomial strain energy potential for  .
.
Denoting the principal stretches by  ,
,  and
 and  (
 (
 ,
, 
 and
 and 
 are the eigenvalues of the right Cauchy-Green deformation tensor) and the deviatoric stretches by
 are the eigenvalues of the right Cauchy-Green deformation tensor) and the deviatoric stretches by 
 ,
, 
 and
 and 
 , where
, where 
 , the Ogden strain energy potential takes the form:
, the Ogden strain energy potential takes the form:
|  | (350) | 
The input deck for a hyperelastic material looks as follows:
First line:
Following line for the ARRUDA-BOYCE model:
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Following line for the MOONEY-RIVLIN model:
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Following line for the NEO HOOKE model:
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Following line for the OGDEN model with N=1:
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Following line for the OGDEN model with N=2:
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Following lines, in a pair, for the OGDEN model with N=3: First line of pair:
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Following line for the POLYNOMIAL model with N=1:
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Following line for the POLYNOMIAL model with N=2:
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Following lines, in a pair, for the POLYNOMIAL model with N=3: First line of pair:
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Following line for the REDUCED POLYNOMIAL model with N=1:
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Following line for the REDUCED POLYNOMIAL model with N=2:
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Following line for the REDUCED POLYNOMIAL model with N=3:
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Following line for the YEOH model:
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Example: *HYPERELASTIC,OGDEN,N=1 3.488,2.163,0.
defines an ogden material with one term:  = 3.488,
 = 3.488, 
 = 2.163,
 = 2.163,  =0. Since the compressibility coefficient was chosen to be zero, it will be replaced by CalculiX by a small value to ensure some compressibility to guarantee convergence (cfr. page
=0. Since the compressibility coefficient was chosen to be zero, it will be replaced by CalculiX by a small value to ensure some compressibility to guarantee convergence (cfr. page ![[*]](file:/usr/share/latex2html/icons/crossref.png) ).
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Example files: beamnh, beamog.
 
 
 
 
 
 
