Multi-objective optimization of a fish-shaped compression-torsion mechanical metamaterial with gradient asymmetry

Abstract Conventional compression-torsion metamaterials have limitations in balancing multidimensional load responses and tunable mechanical properties. To address this issue, this article introduces a fish-shaped compression-torsion mechanical metamaterial (FCTMM) with gradient asymmetry. The mechanical performance of FCTMM is systematically investigated through a synergistic approach combining the gradient design, the finite element analysis (FEA), the experiments (EXP), and the multi-objective optimization. Five types of gradient FCTMM are designed with gradient structures denoted as 1-1-1-1, 1-1-2, 1-2-1, 2-1-1, and 2-2. The 2-2 gradient structure enhances torsional performance significantly, achieving a maximum torsion angle of 16.5° under compressive strain. Pareto-optimal solutions to balance torsion angle and stiffness are identified by the multi-objective optimization framework that integrates response surface methodology (RSM) and the NSGA-II algorithm. Through the FEA and EXP verification, the torsion angle of the optimized design is 13°, and the Young's modulus is 23 MPa. Furthermore, the research reveals programmable nonlinear elastic behaviors, including Poynting effect inversion, thereby enabling tailored mechanical responses. This study holds significant value in the field of smart structures and demonstrates broad application prospects, particularly in aerospace, robotics, and biomechanics.