A level-set shape metamorphosis with mechanical constraints for geometrically graded microstructures

Functional performance benefits brought by graded materials or a variation of microstructures have been established. However, the challenge of connecting the adjacent microstructures remains open. Without connected microstructures, the design is only theoretical and cannot be realized in practice. This paper presents a shape metamorphosis approach to address this challenge. The approach formulates an optimization problem to minimize the difference between two shapes, where the shapes generated during the optimization iterations form the graded microstructures. A stiffness-based constraint is proposed to eliminate potential breakage or shrinkages in generating the intermediate shapes, which are used to build a transition zone for the two shapes to be connected. This also ensures that the optimal functionality is not compromised significantly. A series of numerical studies demonstrate that the proposed approach is capable of producing smoothly connected microstructures for multiscale optimization