This work presents a class of multiscale mathematical and computational formulations as well as homogenization and localization numerical procedures for multiscale modeling of (1) materials with fixed microstructures, (2) problems with evolving microstructures such as stressed grain growth processes in polycrystalline materials, (3) microstructural effect under large deformation, (4) problems with local instability such as wrinkling formation, (5) eigenvalue problems.

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