09 Dec 2016
— Edited @
03 Nov 2021
Here are some questions I encounter recently. I posed these questions for discussion since I think these questions are of interest to everyone work in multiscale simulation, micromechanics. Any thoughts are appreciated if you would like to share.
12 Dec 2016
1. To answer your first question, I think we need to carry out the constitutive modeling at different places where the properties are different. We could have as many constitutive modeling as the total number of elements used in the macroscopic analysis. However, usually, we have to assume some type of local periodicity, which means in the neighborhood of your SG, there are many such SGs. In this sense, we usually have the number of constitutive modeling much less than the number of macroscopic elements.
2. The correct questions shoudl be for porous materials, effective properties are more senstivie to boundary conditions. However, if it is a periodic material, then one unit cell is sufficient with periodic boundary conditions for linear behavior. For nonlinear behavior, then the SG size should be as big as the characteristic length of the nonlinear deformation. The reason to use MSG instead of RVE analysis is that we can do it more efficiently and without worrying about to apply the right boundary conditions. It is noted that one is not free to appy any BCs (SUBC, KUBC, or PBCs), one must apply the best boundary conditions for the homogenization to work. The general guideline is: for a heterogeneous material (periodic or not), if any macro dimension is many times bigger than the SG in that direction, PBC should be applied. Otherwise, our way of relaxing PBC should be used.
3. The applicability of PMIL to nonlinear behavior except hyperelasticity is still under research. We will have more definitive answers in the near future.