Level Set Topology Optimization of Printed Active Composites

Multimaterial polymer printers allow the placement of different material phases within a composite, where some or all of the materials may exhibit an active response. Utilizing the shape memory (SM) behavior of at least one of the material phases, active composites can be three-dimensional (3D) printed such that they deform from an initially flat plate into a curved structure. This paper introduces a topology optimization approach for finding the spatial arrangement of shape memory polymers (SMPs) within a passive matrix such that the composite assumes a target shape. The optimization approach combines a level set method (LSM) for describing the material layout and a generalized formulation of the extended finite-element method (XFEM) for predicting the response of the printed active composite (PAC). This combination of methods yields optimization results that can be directly printed without the need for additional postprocessing steps. Two multiphysics PAC models are introduced to describe the response of the composite. The models differ in the level of accuracy in approximating the residual strains generated by a thermomechanical programing process. Comparing XFEM predictions of the two PAC models against experimental results suggests that the models are sufficiently accurate for design purposes. The proposed optimization method is studied with examples where the target shapes correspond to a plate-bending type deformation and to a localized deformation. The optimized designs are 3D printed and the XFEM predictions are compared against experimental measurements. The design studies demonstrate the ability of the proposed optimization method to yield a crisp and highly resolved description of the optimized material layout that can be realized by 3D printing. As the complexity of the target shape increases, the optimal spatial arrangement of the material phases becomes less intuitive, highlighting the advantages of the proposed optimization method.