Mechanism-driven integration of structure and function in hyperelastic metamaterials via programming fractal-based stress redistribution

The research on hyperelastic flexible structures is trending toward the integration of materials, structures, and functions, as well as toward multi-scale design and parametric design. It is a serious challenge to establish a cooperative design paradigm that simultaneously achieves large deformability, high energy absorption, and functional performance. This paper proposes a fractal-like geometry-based design approach that redistribute stress distributions by tuning the topological configurations of hyperelastic architectures. Based on such stress redistribution, controlled local buckling is induced, and the mechanism underlying the negative Poisson's ratio (NPR) effect is elucidated, thereby realizing the integrated structure–function design. The parametric constitutive model has been developed, which combines strain energy with displacement, incorporating fractal iteration order, dimensionality, geometric parameters, and hyperelastic material based on finite element framework. The proposed theoretical and computational methodology is applicable to 2D, 2.5D, and 3D hyperelastic flexible structures. Experimental results validate the approach, demonstrating that topological fractal design enables excellent synergy between large deformability and high energy absorption. This work establishes a new structural design paradigm for mechanical metamaterials, integrating materials, structures, and functions, and provides a theoretical foundation and a novel conceptual framework for cooperative design in flexible structures, engineering protection, and multiscaled fractal design.