Suppose I have stress and strain relationship and it can be simplified to the equation $\sigma=Function(\epsilon)$. This is the CONSTITUTIVE equation of the material I want to do research.
Assume that I need to do the finite element analysis and it has dynamic(nonlinear) deformation, I have the model and I have the CONSTITUTIVE equation which I mentioned the 1st paragraph.
How can we put those things into a structural equation to do the simulation and what structural equation I need to use?
Can we put this CONSTITUTIVE equation into the following equation $\nabla\cdot \sigma =Force $? Then we can get $\epsilon$, we get displacement and $\sigma$ explicitly.
Also, I think the above is the linear equation, what about nonlinear equation?
Thank you very much.