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Several problems with contact convergence in cell modelling.

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BikerXC

Bioengineer
Aug 3, 2013
3
Hello everyone.

I have been reading this forum for long time to answer most questions I have had. Nevertheless, I haven't found the answer to the following problem:

I am modelling a contact problem consisting of two plates and a cell between them. The top plate is a cantilever beam modelled with shell elements (S4), the lower plate is a rigid body and the cell is modelled with C3D8 elements. Moreover, I am using an UEXPAN subroutine to simulate the cell contraction between those plates. The elastic modulus of the cell is much lower than the cantilever modulus, which could be a problem.

The cell part has double elements divided in two sets: the first one represents the passive behaviour of the cell and the second one is the active behaviour (UEXPAN). This way, I can change the passive behaviour easily (or that was what I was thinking). I have been trying to run three types of passive behaviours: Linear elastic, hyperelastic (Neo-Hookean) and porous elastic. This model works fine with models without contacts, but not with them.

Surpringsinly, the more stable contact model is the porous elastic, but when I use hyperelastic and linear elastic passive behaviour I get convergence problems.

The contact must allow some sliding (I have to define a friction coefficient) with no penetration between surfaces.

I have tried several interaction properties:

*Surface Interaction, name=Lagrange
1.,
*Friction, lagrange
15., %% Here I have a question: Has a friction coefficient above 1 any sense? Some error in abaqus said that could be up to 1E+3 but...
*Surface Behavior, no separation, direct
*Surface Interaction, name=Penalty
1.,
*Friction, slip tolerance=0.005
15.,
*Surface Behavior, no separation, direct
1e+30,
*Surface Interaction, name=Rough
1.,
*Friction, rough
*Surface Behavior, no separation, direct

With these contacts I am trying a step with the following configuration:
*Step, name=Step-1, nlgeom=YES, inc=100000, unsymm=YES
*Static
1e-12, 1., 1e-20, 1.

The material definition is as follows:

For the hyperelastic behaviour:
** Titanio
*Material, name=Cantilever
*Elastic
552960000., 0.22 %With this modulus I obtain a specific stiffness needed to my model.
*Material, name=Kact
*Elastic
10000., 0.45
*Expansion, type=ORTHO, user
*Material, name=Kpas
*Hyperelastic, neo hooke
500., 4850.
*Material, name=Rigid

For the elastic behaviour:

** Titanio
*Material, name=Cantilever
*Elastic
973209600., 0.22
*Material, name=Kact
*Elastic
10000., 0.45
*Expansion, type=ORTHO, user
*Material, name=Kpas
*Elastic
1000., 0.45
*Material, name=Rigid

The model is drawn in microns so the units are Pa (pN/um^2) and pN for forces to be consistent.

I have tried surface-to-surface and node-to-surface discretization method, but as far as I know, surface-to-surface, even though could be slower, it is more likely to get convergence. The slave surface is the cell, which has finer mesh than the master surface, which is the cantilever. I also have tried several mesh refinement without any change in the result. Since I have to manually duplicate the mesh of the cell, adaptative meshing is not an option.

I have a collection of warnings and errors of different kinds depending on how I define the contact. For example:

With linear elastic behaviour, surface-to-surface and node-to-surface discretization method, lagrange, penalty or rough interaction and contact control to stabilize the solution, I get element distortion in very few elements in the top side of the cell and the convergence is judged unlikely.

Using hyperelastic behaviour, with the same configuration as above I get numerical singularity in the cantilver, which is encastred in one side so I don't know how can it be possible because I have fixed all the D.O.F.

I have been working in this model for several weeks but I don't get point. Any help and point of view will be helpful and thankful.

Thanks in advance,

Aaron.
 
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Here I have some specific errors:

1) Using an hyperelastic behaviour, rough interaction, small sliding and surface to surface discretization I get:

***WARNING: THE SYSTEM MATRIX HAS 44 NEGATIVE EIGENVALUES.
EXPLANATIONS ARE SUGGESTED AFTER THE FIRST OCCURRENCE OF THIS MESSAGE.

***WARNING: SOLVER PROBLEM. NUMERICAL SINGULARITY WHEN PROCESSING NODE
CANTILEVERSHELL-1.1104 D.O.F. 2 RATIO = 114.817E+09 .

***WARNING: THE AVERAGE FORCE USED TO ENFORCE CONTACT CONSTRAINTS AT NODE
CELL2-1.178 IS 625.438E+06 TIMES LARGER THAN THE AVERAGE ON THE
OTHER ELEMENTS IN THE MODEL.

***NOTE: THE SOLUTION APPEARS TO BE DIVERGING. CONVERGENCE IS JUDGED UNLIKELY.

***ERROR: TOO MANY ATTEMPTS MADE FOR THIS INCREMENT

2) Using an hyperelastic behaviour, lagrange interaction, finite sliding and node to surface discretization I get:

***WARNING: EXCESSIVE DISTORTION AT A TOTAL OF 784 INTEGRATION POINTS IN SOLID
(CONTINUUM) ELEMENTS % Only in first increment

***NOTE: THE RATE OF CONVERGENCE IS VERY SLOW. CONVERGENCE IS JUDGED UNLIKELY.

***ERROR: TOO MANY ATTEMPTS MADE FOR THIS INCREMENT
 
The parte with the numerical singularity is a cantilever beam encastred in one end. It has an elastic modulus of 552 MPa, while the cell, that is pulling on the other end, has 10 kPa.

It works fine with rough contact and linear elastic behaviour, and lagrange contact with porous elastic behaviour. However, hyperelastic behaviour doesn't achieve convergence with either contact types, same way as linear elastic with lagrange contact.

I have checked the set of nodes with warnings and they are placed in the contact. I have checked the contact definition to avoid constraint duplication on this part, but this doesn't seem the problem.
 
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