To reduce the fem model, I use the concept of symmetry and the applied constitutive model is the Mohr - Coulomb model (non - linear). According to "Concepts and applications of finite element analysis, Cook, et.al." can generate unwanted solutions. I need to justify that the model is approximate and can be considered correct despite the aforementioned.
Help please....
I don't know the precise context in which the recommendation was offered, but in principle there is no conflict between symmetry and non-linearity, providing both remain applicable throughout the problem. Make sure though that symmetry really applies and that its numerical imposition does not prevent the development of possible non-symmetric solutions (such as bifurcations, shear banding, buckling, etc.).
You should provide more details about your problem. Symmetry is rarely in conflict with nonlinear problems.
A model of a soil deposit that has been reduced by symmetry to 1/4 of the model has been made. The constitutive model used is the Mohr Coulomb model, which is an elastoplastic model. However, a reviewer tells me that when working with a non-linear constitutive model, geometry reduction should not be done by symmetry because undesirable results are obtained according to "Concepts and applications of finite element analysis, Cook, et.al. "
You could run a simplified complete model and the same model with symmetry, and you can show that the results are comparable.
I am not recommended using symmetry to reduce the model. In nonlinear domain you can not extend your result on one part to whole area. Specially if your model has material nonlinearity.
Dear Pedrazzi,
Thank you very much for your attention to my answer. The cases you posted, as I understand, are linear cases. In linear cases you can use superposition method and if the loading and geometry both are symmetry, you can use a portion of system to analyze it for whole system. But if the system for any reason is nonlinear you can not use superposition method.
Let me to explain the second picture that you sent. In that case the deflection was calculated based on y''(x)=M(x)/EI. The analysis here is based on separating reactions by superposition analysis and calculating the deflection. But what if we have a large deflection which means y''(x)=M(x)/EI(1+y'(x)^2)^1.5 and the material is not linear and its moment of inertia varies based on a nonlinear function? You can not separate reactions and you can not calculate deflection by superposition. So the deflection at each point will be a nonlinear function of its position and most probably deflection will be nonsymmetric.
The most famous paper is:
http://pilch.us/papers/Large%20Deflection%20of%20Cantilever%20Beams.pdf
I agree with Claudio.
If the geometry, loads and constraints are symmetric, and the material response is isotropic (linear or nonlinear), you can use a symmetric model.
There may be symmetry in an anisotropic and even heterogeneous materials. We have modeled bamboo culms, which are anisotropic and heterogeneous, but of course there is symmetry in the properties with respect to a system of cylindrical coordinates.
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