Concurrent cross-scale and multi-material optimization considering interface strain gradient

The existing topology optimization methods are mostly based on traditional continuum mechanics approaches to deal with cross-scale and multi-material problems considering interfaces. Unfortunately, the inability of traditional continuum mechanics models to capture the size dependence of microscale structural deformation behavior limits their application in the optimization design of advanced micro and nanostructures. Hence, a new cross-scale optimization of multi-material structures considering interface is proposed based on Wei-Hutchinson strain gradient theory, which could describe and explain the size dependence during optimization process. Firstly, a new interpolation scheme is developed to identify interfaces between two arbitrary materials and ensure precise control of the interface width. Then, through geometric adaptive projection techniques, the behavior at the interface and the macro-micro mechanical behaviors are cleverly projected and solved within a nine-node quadrilateral finite element set. After that, the geometric parameters of adaptive geometric components under the framework of the movable deformable component method introduce non-periodic infill microstructures into multi-material topology optimization considering interfaces, achieving minimization of compliance. Results show that the compliance of the non-periodically infilled microstructure multi-material layout can be significantly improved by considering size effects compared with periodically uniform infilled microstructure multi-material layouts in the process of cross-scale optimization. Furthermore, the new optimization algorithm can effectively control the stress levels of the overall structure as well as the stress at the interfaces of heterogeneous materials, thereby reducing the stress concentration effects in critical stress region.