problem of parameters

[YunfeiWang]

Dear all
 
      I download the user material subroutines writed by Prof. S. Govindjee(see the fortran files in attachment). And the description of the consitutive equation is

shown as the picture in attachment. Could you tell me what the three parametes "μ" ," I_sym " , "1" behind beta in  equation (2) are ?

Thank you very much

Best regard

[FEAP_Admin]

You should grab a copy of a basic book on continuum mechanics to understand the tensor notation.

[YunfeiWang]

You should grab a copy of a basic book on continuum mechanics to understand the tensor notation.

       But there is not exist “γ”(gamma) and instead of that it exist a “μ”(mu)  in equation (2).  And I do not know whether the "1" which behind β is Arabic numerals

1 or  others ?  So I  doubt that there are some error in equation (2).

[K.Li]

"μ" is a material parameter in the Saint Venant–Kirchhoff model

https://en.wikipedia.org/wiki/Hyperelastic_material

from http://faculty.ce.berkeley.edu/sanjay/,

"In this alpha, beta, and gamma are the 3 cubic constants"

The boldface "1" in (2) is the second order unit tensor, and " Isym " is the fourth order unit tensor.

Check the book Nonlinear Solid Mechanics (https://www.amazon.com/Nonlinear-Solid-Mechanics-Continuum-Engineering/dp/0471823198) for more information

[YunfeiWang]

"μ" is a material parameter in the Saint Venant–Kirchhoff model

https://en.wikipedia.org/wiki/Hyperelastic_material

from http://faculty.ce.berkeley.edu/sanjay/,

"In this alpha, beta, and gamma are the 3 cubic constants"

The boldface "1" in (2) is the second order unit tensor, and " Isym " is the fourth order unit tensor.

Check the book Nonlinear Solid Mechanics (https://www.amazon.com/Nonlinear-Solid-Mechanics-Continuum-Engineering/dp/0471823198) for more information

Dear K.Li
   
   Thanks for your apply. But I could not find the parameter gamma in (2).

Best Regards

[K.Li]

You should check the code yourself, 'gamma' is in the code.

Code: [Select]

c       Set up the moduli

        alpha = ud(1)
        beta  = ud(2)
        gamma = ud(3)
        tmpx = alpha - beta - 2.d0*gamma
No body will help you if you do not read the code.

[YunfeiWang]

You should check the code yourself, 'gamma' is in the code.

Code: [Select]

c       Set up the moduli

        alpha = ud(1)
        beta  = ud(2)
        gamma = ud(3)
        tmpx = alpha - beta - 2.d0*gamma
No body will help you if you do not read the code.

Thank you for you answer

I also read the code. In the code, there is no any parameter mu but there is the parameter gamma.Also there is the parameter "tmpx=alpha-beta-2.d0*gamma"

in the code  which is same as "α-β-2μ" in (2). So I think that the mu in (2) is the gamma in the code. In fact , I just want to know whether my thought is true?

Best Regards

[Prof. S. Govindjee]

The best way to figure this kind of stuff out is to create a test case to which you think you know the exact answer.  Then run the code, print out some debugging information, print out the results and then compare to your exact answer.  This will tell you what it is doing.