UMAT Simple linear viscoelastic example 1

[qiangbo]

Hi,

I am studying the UMAT manual. The shipped example for modeling viscoelastic material gives a lot of insights. But I have a question:

What is relationship between the parameters for the model (mu1, E1 and E2) and the parameters to the subroutine (lambda, mu, lambda_hat, mu_hat and nu)?

Thanks!

 

[bvrm22]

Hi,

In the example you have a ode of the form:
Sigma + A *dSigma = B*eps + C*deps

A is obviously nu_tilde.
B and C are split into lame coefficients by using the poisson coefficient nu_p. A value for nu_p must be chosen for your material. Eg. Steel has 0.3. The poisson coefficient helps to convert the proposed 1D visco-elastic model with springs and dampers into a multidimensional model for 3D or 2D analysis.

Eg. Splitting B, knowing the value of B and a value for poisson nu_p
There are 2 equations:
1) B = lambda + 2*mu
2) mu_p = lambda/(2*(lambda + mu)) (see definition lamé coefficients)

Solve this system of linear equations for lamda and mu and you’ll know their values. (Analogue for splitting C).

Kind regards,
bvrm