# How to model non linear governing equation in FEA?

1. Apr 6, 2013

### hihiip201

Hi:

in a linear spring model for materials, the governing matrix equation is K * U = F

where K is the material stiffness AE/l , u is the displacement at each nodes and F is the force in the discretized elements.

but this is only true for a linear spring, what if I have some non linear spring? I know there's no such thing but what if I now have some other physics that I would like to model that involves a non linear governing equation? how would I model my matrix?

thank you

hihiip201

2. Apr 6, 2013

### AlephZero

You have that backwards. In real life there is not such thing as a linear spring, but linear is a good enough approximation for a many purposes.

For an elastic nonlinear material, you can make E a function of the strain in the material. You need to do an iteration until the solution converges with consistent values of E and the strain.

If the material behavior is plastic (i.e. when you remove the loads, the displacements do not return to zero), that is too complicated to explain how to model it here - get a textbook on nonlinear FE analysis!

3. Apr 6, 2013

### hihiip201

But with E as a function of strain (so I guess i will have something like: K u^n = F.)

can I call u^n at some node constant and then solve the system like it was still linear?

or do I have to do :

logK + n logn = log F to generate a matrix?

thanks

4. Apr 9, 2013

### SteamKing

Staff Emeritus
In a progressive rate spring, k increases as the spring is compressed.