Elmer Discussion Forum

Hi,

We have updated the devel version of the ElasticSolve module today so that the solver of Elmer can output user-defined state variable fields (with "Output State Variables = True") to a result (vtu) file and then they may be visualized as usual. The way how UMAT variables are created and handled internally has also changed (the UMAT variables are now generic Elmer fields created with a flag -ip which means that their values are associated with the integration points).

-- Mika

Thank you.

I shall try this out.

Kevin

This version puts the invariant values max strain, mid strain, min strain, max principal stress, mid, min, and mises into the state variables
7 state variable. Output State Variables = True outputs them to the vtu file.
Thank You, Mika. This makes for better post processing.

Another modification added a sixth material constant to specify an ultimate stress where the material will go perfectly plastic. If perfectly plastic is not required just make it a large number.

Hi,
I'm very interested in this topic. In particular, my case study is a rotating plane disc of steel subjected to its centrifugal force only.

Which is the mathematical formulation behind the bi-linear material solver?
I know how the elastic solver works and its formulation. However, I don't know how the bilinear material can be handled.

Is it sufficient to set E as a function of strain in the equation below and solve it iteratively? (I don't have deep knowledge of mechanical theory, I come from the electric world)

sigma = E(strain)/(1-nu^2) * [1 nu 0; nu 1 0; 0 0 (1-nu)/2 ]

Do you have any good references?

Thanks

The bi-linear model uses a stress-strain curve Stress is the vertical axis and strain is the horizontal axis. E is the slope of the curve, change in stress over the change in strain. Bi-linear means the stress strain curve is modeled with two linear curves of a different slope, the initial slope is the liner E of the material until yield, then the second curve represents the plastic behavior. The user routine uses point input from the sif to define the stress strain curve. Calculates E and the stresses.

To make a better model of the stress strain curve a piecewise curve using more data points could be used.

viewtopic.php?t=6943

Hi,

thanks for your answer. Good to know that a piecewise curve can be used.
Actually, what I would like to know is if, in 2d-plane stress, the relation between stresses and strains is still the equation
below with only the exception that E is not constant but depends on strain values.

[sigma] = E(strain)/(1-nu^2) * [1 nu 0; nu 1 0; 0 0 (1-nu)/2 ] * [strain]

where [sigma] = (sigma_x, sigma_y, sigma_z) and [strain] = (strain_x, strain_y, strain_z)

Thanks

Yes the equations are true, E is not constant. But you need E to calculate the strain. The stress strain curve defines the relationship between stress and strain for a given material, which determines E. You have to know two of the values to calculate the third, or you have to know the path you want to stay on. Otherwise there are an infinite number of curves that will satisfy the equation.

The usual approach is you do a tensile test of the material to determine a stress-strain curve. Or you use a stress-strain curve already developed by such a test.

The equations hold for steel, aluminum, gold, etc. So if you do not know E or the relationship between stress-strain, how do you what material you are analyzing?

Ok, the stress-strain curve is known.
From the solver's point of view, I think the solution should be obtained with some iterations using the Newton-Raphson method starting from an initial guess as occurs in electromagnetic problems with nonlinear ferromagnetic materials.
I'm not talking about Elmer but a general point of view.
In my formulation, the unknown is the displacement "u".
I should be able to do some iterations until the error is below a certain tolerance.

Thanks

If the stress-strain curve is known then yes.