gridap / gridap/Gridap.jl

Issue in Tutorial 5 (Hyper-elasticity) Using Different Material Constants

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Description

I have an interest in solid mechanics and have been looking at the representative tutorials provided by Gridap. When I tried changing up the material parameters for Tutorial 5 (Hyper-elasticity) to different material parameters, I ran into a convergence issue.

The $\lambda$ (Lame) and $\mu$ (shear modulus) parameters are rather small, but that doesn't appear to be the issue. Using the values of $\lambda=100$ and $\mu=1$ and converting them into corresponding values in linear elasticity gives $E=2.96$ (Pa) and $\nu=0.495$. Now, there isn't an issue with poisson's ratio being 0.495, but slightly lower values are also realistic for hyper-elastic materials. As such, I decided to set $E=100$ and $\nu=0.45$, which means the original two parameters are (approximately) $\lambda=310.3$ and $\mu=34.48$.

Note, I changed the following items in the tutorial:
-$\lambda=310.344827586207$
-$\mu=34.48275862068966$
-partition = (300,300)
-disp_y = disp_x
-disp_x = 0.1*disp_x
-g1 = VectorValue(disp_x,disp_y)

For a coarse enough mesh (<=250 elements/side for the hypercube in the example), there doesn't appear to be an issue for solving the problem. However, once the elements/side is >=300, there ends up being a convergence issue that ends up blowing up the calculation. Looking at the bottom-right edge (that is being moved upwards due to the updated boundary conditions, it appears as though there is a small wrinkling before the calculation "blows up".

The issue appears to occur solely when I drop $\nu$ from 0.495 to slightly smaller values (e.g. 0.45 or 0.4) when I increase the mesh size. I am concerned about what might be happening and I want to understand what's going on to prevent the issue from happening again when I try to solve more than just a toy problem. I was wondering if anyone had any insight as to what in the numerical implementation might be causing this issue. I have attached the modified julia script as a txt file.

Thank you for your thoughts and help.
[hyperelasticity.txt](https://github.com/gridap/Gridap.jl/files/10703081/hyperelasticity.txt)

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