A multi-scale formulation for modeling of wrinkling formation in polycrystalline materials

This work aims to develop multi-scale mathematical formulation and computational algorithm for modeling microstructure evolution and wrinkling formation in polycrystalline materials. A multi-scale variational formulation based on asymptotic expansion method, as well as associated numerical methods are presented. Proposed is a consistent homogenization method that yields a tangent operator with major symmetry. The homogenized material response tensors vary in space in the macroscopic structures. This feature captures the local instability when the regional deformation gradient reaches certain ill-conditioned (non elliptic) state. Moreover, it is shown that the conventional non interactive single-scale homogenization approach is incapable of capturing the localized winkling response.