Mooney-Rivlin Model - LS-DYNA MAT_027
In this rubber model, the strain energy density is defined as the function of right Cauchy-Green tensor
where A, B are two material constants, and
Parameter Identification
There are two constants in this model. So we can identify them if knowing two test points in uniaxial tension. To get a useful equation, the principal stresses can be derived from strain energy function by the partial derivative as
To remove the Jacobian terms,
Since
Now using this equation, if we know the two engineering stresses at the each stretch ratio, the two constants, A and B can be determined by performing least square fit to the two points.
For example, a material description is obtained like the following table, then you know the engineering stresses,
Tensile stress at 100% | 2.06 MPa |
Tensile stress at break | 4.10 MPa |
Elongation at break | 380% |
Using stretch ratio definition,
Engineering stress-strain curve can be predicted from above parameters in uniaxial tension as below:
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