Siros Khorshidi, Zia Saadatnia
Abstract Due to their tunable mechanical properties and broad applicability, three dimensional compressible–twistable mechanical metamaterials (3D-CTMM) have attracted significant attention in recent years. While the recent research on these configurations is limited to linear mechanical behavior analysis, the nonlinear characteristics of these metamaterials are crucial in practical applications such as adaptive vibration isolation, impact protection, and energy harvesting. This study introduces a combined nonlinear stress–strain relationship and strain-energy-based analytical framework, supported by finite-element analysis and experimental validation for investigating the nonlinear mechanical load-deformation behavior of a 3D-CTMM, with potential applicability to a broader class of the 3D-CTMM designs. The constitutive model and coupled load-deformation and load-torsion responses of the unit cells are investigated by incorporating the intrinsic material nonlinearity and complementary strain energy theory into the analysis and then expanded to the overall phase of the 3D-CTMM. The accuracy of the mechanical modeling is evaluated through both numerical simulations and experimental characterization. The results demonstrate strong agreement across the multiscale analyses and reveal pronounced nonlinear behavior in the deformation responses particularly in relatively high global strain values of up to 16 % . The nonlinear behavior suggests that the conventional assumption of constant Young’s modulus and Poisson’s ratio for the overall phase of the 3D-CTMM may not fully capture the response, as these parameters vary with nonlinearity and depend on the number of unit cells in the configuration. Furthermore, as a tangible application, the capability of the studied 3D-CTMM to absorb impact energy is also presented where a 3 × 3 × 3 assembly fabricated by thermoplastic polyurethane exhibits superior potential for absorbing impact energy.