Recent advancements in manufacturing, finite element analysis (FEA), and optimization techniques have expanded the design possibilities for metamaterials, including isotropic and auxetic structures, known for applications like energy absorption due to their unique deformation mechanism and consistent behavior under varying loads. However, achieving simultaneous control of multiple properties, such as optimal isotropic and auxetic characteristics, remains challenging. This paper introduces a systematic design approach that combines modeling, FEA, genetic algorithm, and optimization to create tailored mechanical behavior in metamaterials. Through strategically arranging 8 distinct neither isotropic nor auxetic unit cell states, the stiffness tensor in a 5 × 5 × 5 cubic symmetric lattice structure is controlled. Employing the NSGA-II genetic algorithm and automated modeling, we yield metamaterial lattice structures possessing both desired isotropic and auxetic properties. Multiphoton lithography fabrication and experimental characterization of the optimized metamaterial highlights a practical real-world use and confirms the close correlation between theoretical and experimental data.

The equilibrium forms of pantographic blocks in a three-point bending test are investigated via both experiments and numerical simulations. In the computational part, the corresponding minimization problem is solved with a deformation energy derived by homogenization within a class of admissible solutions. To evaluate the numerical simulations, series of measurements have been carried out with a suitable experimental setup guided by the acquired theoretical knowledge. The observed experimental issues have been resolved to give a robust comparison between the numerical and experimental results. Promising agreement between theoretical predictions and experimental results is demonstrated for the planar deformation of pantographic blocks.

The central theme of this study is to investigate a remarkable capability of a second-gradient continuum model developed for pantographic structures. The model is applied to a particular type of this metamaterial, namely the wide-knit pantograph. As this type of structure has low fiber density, the applicability of such a continuum model may be questionable. To address this uncertainty, numerical simulations are conducted to analyze the behavior of a wide-knit pantographic structure, and the predicted results are compared with those measured experimentally under bias extension testing. The results presented in this study show that the numerical predictions and experimental measurements are in good agreement; therefore, in some useful circumstances, this model is applicable for the analysis of wide-knit pantographic structures.