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 leads to the same behavior as long as the
std is high), with no structure such as layers or anything else. In this case,
the system should clearly be macroscopically isotropic (up to statistical
fluctuations due to the random properties) for symmetry reasons.
At least in the limit h->0 I agree. For finite mesh sizes, I would expect that
the material has a degree of anisotropy that goes to zero as you make the mesh
smaller. It is true that the axes of anisotropy should be oriented in random
ways for different realizations of the same experiment on the same mesh. When
you do your computations, have you checked (for different realizations of the
random process):
(i) whether the orientation of anisotropy is always the same, and always
related to the principal directions of the mesh?
(ii) how the magnitude of anisotropy behaves as you refine the mesh?
Best
W.
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Wolfgang Bangerth email: [email protected]
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