Nonlinear Finite Element Analysis: When & How

[chandran]

what is a non linear finite element finite element analysis. When does a structure behave non linearly and how do we calculate non linearity
of an element by the nodal displacements.

 

[Astronuc]

Think of elastic vs plastic mechanics, as one example. Once an elastic material goes beyond yield, where $\sigma$=E $\epsilon$, then it develops a nonlinear behavior.

Then there are also cases with temperature/thermal gradients, strain rate effects, and internal viscosity/friction. And then there is cracking and multiple phases.

To model these, one simply needs a good constitutive model and very good properties models.

Think about the size of the FEA mesh elements vs the grain size of a polycrystalline material.

 

[PerennialII]

... and if we limit ourselves to, say, quasistatic structural applications the other major source on nonlinear behavior (other than material one which is the more typical one, and as indicated above, the far more diverse one) is geometric nonlinearity = large deformations, which you can understand essentially resulting when the deformations can't be uncoupled from the solution (or probably easier = the deformations become large enough to affect the solution itself). This is something occurring most easily for example with cracks & fracture mechanical analyses and damage mechanical material models.

 

[LeBrad]

what is a non linear finite element finite element analysis.

Are you talking about finite element methods for nonlinear systems, or a nonlinear finite element method, i.e. cubic basis functions? Or is that the question you are asking.

how do we calculate non linearity of an element by the nodal displacements.

I don't think I understand what you are trying to do. It sounds like you want to fit nonlinear functions to measured data? But that wouldn't be FEM, because FEM is just a method for solving equations that you already know. And if you want to determine how nonlinear your system is, you're probably better off just looking at the equations you're dealing with.