Design of active materials distributions for four-dimensional printing based on multi-material topology optimization

Printed active composites (PACs) are capable of deforming from an initial shape to a target shape via spatial arrangements of active materials within a passive matrix. Multi-material polymer printers allow precise placement of multiple materials in the design space. However, single active material is difficult to satisfy the demand in the high-precision matching of more complex target shape. Hence, a multi-material topology optimization approach for the design of PACs is proposed to achieve a target shape under a given stimulus. A multi-material interpolation function for active materials is established, and continuum mechanics modeling is used for simulating active material behaviors on a voxel basis to compute deformations for a given material distribution. The adjoint method is used for sensitivity analysis. Numerical simulations, of different target shapes with the same initial shape, verify the effectiveness of the method. The proposed method is feasible in the conceptual designs of PAC material distributions benefit with stable convergence, ease of implementation, and low computational costs.