### Re: [deal.II] Mesh-induced elastic anisotropy and distorting the quad. points as a way to palliate it

Hi Sebastian, first of all, sorry for my late reply. Thank you very much for comment, it certainly raises some very interesting points. I think the only thing which is still left to be explained is the fact that a triangular grid, which yields the right isotropic result, becomes anisotropic

### Re: [deal.II] Mesh-induced elastic anisotropy and distorting the quad. points as a way to palliate it

Hi David, I'm neither an expert, nor do I know the literature well, but looking on your pictures, I think, the situations you are studying are geometrically anisotropic. Just plot the distribution of angles the faces of your inhomogenities make with the x-axis. For the quad-case, you'll get two

### Re: [deal.II] Mesh-induced elastic anisotropy and distorting the quad. points as a way to palliate it

On 7/10/20 9:15 AM, David F wrote: I have a 2D system for which I create the stiffness tensor of an isotropic material, but for each finite element I create it with a different shear modulus. The shear modulus is random for each element (I use an exponential distribution, but any distribution

### Re: [deal.II] Mesh-induced elastic anisotropy and distorting the quad. points as a way to palliate it

I have a 2D system for which I create the stiffness tensor of an isotropic material, but for each finite element I create it with a different shear modulus. The shear modulus is random for each element (I use an exponential distribution, but any distribution leads to the same behavior as long

### Re: [deal.II] Mesh-induced elastic anisotropy and distorting the quad. points as a way to palliate it

On 7/2/20 10:06 PM, David F wrote: *_Q2_:* why the system behaves as anisotropic if its local inhomogeneous elastic properties are isotropic? If you have any comment or suggestion about the problem of mesh-induced elastic anistropy in FEM, I would like to know it. I don't know how exactly

### [deal.II] Mesh-induced elastic anisotropy and distorting the quad. points as a way to palliate it

Hello everyone, I'm trying to solve a 2D solid mechanics homogenization problem, in which I have element-wise constant elastic properties, which are inhomogeneous and isotropic from element to element (i.e., I am assembling the system using the same 4-rank stiffness tensor for all the