Good mourning,
I have been conducting a FEM analysis to a particular problem using a cohesive model (CZM), i don't want to bother people with details i just have a question about a possible and existing equivalence between problems of failure with displacement based BCs and force based BCs when using a CZM models, BCs : boundary conditions.
In some commercial FEM codes, a displacement based FEM model is more advantageous than a force based FEM model, because a displacement based model doesn't generaly produce convergence problems and instabilities especially if we use an incrimetal procedure with small incriment size.
In the modeling by FEM of an elastoplastic uniaxial tensile test of a specimen, the experimetal test is conducted under displacement imposed to the grips of the machine. The suitable FEM model is a model with an applied displacement BCs. The response of the model can be obtained by the Stress-strain curve, stresses are computed by the ratio between the internal reaction forces victor to cross section of the model or the section of the ligament.
In a same fashion, we attempted to used a FEM analysis to validate results obtained by an analytical method, it is a structure containing a crack and a load (a stress) applied to the upper boundary, results are obtained in term of Load-Crack length curves.
Using a commercial FEM code a similar FEM model was made and instead of a Stress applied to the upper face, a displacement was applied to the same boundary and the stress at the initiation of failure was computed from output of the total reation forces devided by the cross section area of the ligament.
The results were comparable to that obtained by the analytial method.
I have been wondering whether such confrontation is possible since we have made a FEM model with displacement applied boundary conditions.
Hi Amine,
When you impose the displacement on the free edge, you can measure as output from FEM the necessary force and the stress distribution for a finite number of increments of the imposed displacements. For other values of displacements, the necessary force can be obtained by interpolation.
When you apply the force on the free edge, the situation is the same as previously, but with with the forcethe and displacement interchanged.
If there are no errors in the two analyses, the results shall be very close. A possible error could be to not ensure compatibility in displacements for the free edge.
Best regards,
Viorel
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