Hi everyone,
I am performing a static analysis in ANSYS APDL to simulate a silicon component subjected to large deformation.
The undeformed configuration reproduces a portion of an annulus and consequently a cylindrical coordinate system (r,th,z) has been adopted, as depicted in the alleged file SVEA (a). Both the inner and outer radial surfaces R1 and R2 are constrained so as no node can experience displacement along the radial direction, see SVEA (a). The tangential surface T1 is constrained so as no node can experience displacement along the tangential direction, see SVEA (a). Finally, the bottom surface Z1 is constrained so as no node can move along the vertical direction as in SVEA (b). Hence the dimensionality of the problem is three with a plane strain condition.
We are interested in the stress-strain relationship when the system passes from the initial state to the desired configuration depicted in SVEA (c), that is when the angular extension of the annulus undergoes a reduction DELTA_TH, of about the 50% of the intial angular value.
The silicon constituive behavior is modeled through a two-parameters Mooney-Rivlin formulation. Furthermore, incompressibility is also imposed. The element type is SOLID185 with the default full integration option.
Displcament of the T2 surface is progressively imposed through substeps so as to meet convergence requirements. To adequately choose the mesh size and the number of load steps I started with attempt simulations, by imposing smaller angular rotations. The outcome of the simulations is that for:
- angular deformations less than 10%, there is convergence, despite the following warning "Hyper-elastic material may become unstable, material number 1 at temperature 0";
- angular deformations above 10% no solution is available because "One or more elements have become highly distorted [...]".
In the latter case, it seems that a hourglass effect appears, as shown in the figure SVEA (d). For the moment, I have tried to increase the number of load steps and the density of the mesh, but still no result is obtained.
On the other side, I simulated the same problem on a straight geometry and in that case I have a converged solution even for the extreme case of 50% of deformation.
Do you have any suggestion to reach convergence?
Thanks in advance for your attention.
"Hence the dimensionality of the problem is three with a plane straincondition."
Why to use 3D modeling? If you are in plane strain, the model is plane (2D).
An alternative is generalised plane strain, in which the model is still 2D
Dear Denis Benasciutti,
I have also followed your suggestion, and formulated the problem in two dimensions. A SHELL281 element was chosen as long with the same material model and parameters.
Still, convergence is not reached. From the plot of the nodal displacement (see attached figures), it appears that the radial constraint is not satisfied.
Thank you again
a "shell" element is 3D (it has 6 dof in each node).
For a plane strain analysis, use a quad element (4 or 8 nodes)
Dear Denis Benasciutti ,
I have forgotten to mention that I made use of membrane option (KEYOPT, 1, 1). Accordingly, the element is supposed to have translational dof only. The problem that now arises is that the deformed configuration does not meet the imposed constraints, since radial displacements appear.
Thank you
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