Programming and physical realization of extreme three-dimensional responses of metastructures under large deformations

Structures and materials with programmable mechanical responses are desirable for many applications. Great advancement has been achieved and led to the discovery of metastructures/metamaterials with unconventional programmed properties. While most established studies focus on two-dimensional (2D) or pseudo-three-dimensional systems, certain complex deformations and functionalities can only be realized in three-dimensional (3D) space. The lack of comprehensive exploration of programmable large-deformation kinematics in 3D space could leave out a plethora of 3D deformation mechanisms, structural geometries, and complex responses that may lead to unprecedented mechanical functionalities. Based on multimaterial inverse design by topology optimization, this study systematically investigates several precisely programmed nonlinear extreme responses in 3D structures under finite deformations. Sophisticated 3D geometries with unique deformation capabilities are discovered. Under monotonic loading, extreme behaviors such as self-recovering counter-rotation and sequential lateral expansion–contraction are created, which are beyond the reach of 2D structures. The associated mechanisms fully exploit 3D space and optimally harness free-form geometries, material nonlinearity, the large disparity in material properties, and large rotations to deliver the target responses. Some discovered mechanisms are heterogeneous in space and asynchronous in time, spatially consisting of a series of sub-mechanisms. Albeit with complex geometries, the optimized structure with multi-phase and heterogeneous mechanisms is accurately fabricated through a proposed hybrid fabrication method tailored for 3D geometries combining 3D printing and casting, and the design's unique programmed behavior is validated. The experimentally measured response shows high agreement with the prescribed target and numerically programmed responses. The discovered unique 3D deformation patterns and designs, underlying mechanisms, tailored 3D fabrication approach, and experimental procedures could provide meaningful mechanics insights and guidelines for realizing function-oriented mechanical metastructures/metamaterials that fully harness 3D space.