# AceFEM: Divergence in iterative procedure (Newton-Raphson) for fine meshes

I am trying to model a problem of a nearly incompressible $$10~\rm{m} \times 2~\rm{m}$$ beam with a uniformly distributed end load. The beam has a Young's modulus of $$200~\rm{Pa}$$ and a Poisson's ratio of $$\nu=0.49995$$ and I am using a mixed displacement-pressure (Q1P0) formulation with a perturbed Lagrangian approach.

I am using meshes of $$2^N \times 2^N$$ Q1P0 elements and for $$N\leq6$$ to solution procedure is working fine. However, for $$N>6$$ the procedure diverges very early on. I have tried changing the initial load and the load step size in the solution procedure, and I have tried changing the material properties. Whatever I try I cannot get the solution procedure to work for $$N>6$$, which is a problem because I need solutions for at least up to $$N=8$$.
Note: The solution procedure works fine with standard Q2 elements for $$N=8$$ and I can't figure out why it doesn't work for the Q1P0 elements.

The solution procedure I am using is given below (unfortunately I don't know how to make the Greek characters display properly in the code block)

SMTAnalysis[];
tolNR = 10^-5;
maxNR = 500;
targetNR = 100;
\[Lambda]Max = 1;
\[Lambda]0 = \[Lambda]Max/1000;
\[CapitalDelta]\\[Lambda]Min = \[Lambda]Max/10000;
\[CapitalDelta]\[Lambda]Max = \
\[Lambda]Max/100;

SMTNextStep["\[Lambda]" -> \[Lambda]0];
While[
While[
step =
SMTConvergence[tolNR,
targetNR, \[CapitalDelta]\[Lambda]Min, \
\[CapitalDelta]\[Lambda]Max, \[Lambda]Max}]
, SMTNewtonIteration[];
];
If[step[] === "MinBound", SMTStatusReport["Analyze"];
SMTStepBack[];];
step[]
, If[step[], SMTStepBack[];];
SMTNextStep["\[CapitalDelta]\[Lambda]" -> step[]]
];


Plotting the displacement of the end of the beam against $$N$$ yields the following It is clear that the behavior is good up until $$N=6$$.

The element code and notebook in which problem is solved (including solution procedure) are available here:
Q1P0 element
Convergence Test

Any help in improving the solution procedure would be appreciated!

• Is Young's modulus 200 Pa or 200 GPa? Jul 23, 2021 at 10:13
• The Young's modulus is 200Pa. Jul 26, 2021 at 7:14

• This is looks like comment, not like an answer. Could you focus on $\nu=0.49995$, not on $\nu=0.5$? Jul 23, 2021 at 10:05