Analysis and optimization of heterogeneous materials using the variational asymptotic method for unit cell homogenization

The variational asymptotic method for unit cell homogenization is used to find the sensitivity of the effective properties of periodically heterogeneous materials, within a periodic base-cell. The sensitivities are found by the direct differentiation of the variational asymptotic method for unit cell homogenization (VAMUCH) and by the method of adjoint variables. This sensitivity theory is implemented using the finite element method and the engineering program VAMUCH. The methodology is used to design the periodic microstructure of a material that allows obtaining prescribed constitutive properties. The microstructure is modeled as a 2D periodic structure, but a complete set of 3D material properties are obtained. Furthermore, the present methodology can be used to perform the micromechanical analysis and related sensitivity analysis of heterogeneous materials that have 3D periodic structures. The effective material properties of the artificially mixed materials of the microstructure are obtained by the density approach, in which the solid material and void are mixed artificially.