Physics-guided inverse design of bio-inspired network metamaterials via a general non-linear mechanical framework for arbitrary curved-beam lattices

Biological soft tissues achieve a remarkable balance of compliance, toughness, and durability through their hierarchical fibrillar architectures, giving rise to nonlinear mechanical responses such as the characteristic J‑shaped stress–strain curve. Inspired by these natural designs, periodic network metamaterials composed of curved beam elements have become promising candidates for soft robotics, bio‑integrated electronics, and tissue engineering. This emergence underscores the need for a rigorous theoretical framework capable of guiding the rational design of biomimetic architectures and predicting their nonlinear mechanical behavior. Prevailing theoretical models, however, are typically formulated for specific, idealized geometries, limiting applicability to more general and complex network architectures and hindering accurate capture of multiscale deformation mechanisms essential for biomimetic performance.To overcome these limitations, a generalized nonlinear mechanical framework is presented in this study to characterize periodic networks of arbitrarily shaped curved beams, systematically capturing the hierarchical transmission of mechanical responses by bridging individual beam mechanics with lattice‑level interactions under finite extension. The predictive capability is substantiated through finite element simulations and experimental validation across a wide spectrum of network configurations and loading conditions. Building upon this physically grounded framework, an efficient inverse design methodology enables precise tailoring of network architectures toward targeted mechanical specifications. In contrast to data-driven paradigms reliant on extensive training datasets or opaque neural architectures, the proposed approach combines computational efficiency with transparent physical interpretability. Collectively, this work provides a robust theoretical foundation and practical design paradigm for optimizing soft network metamaterials, offering a principled pathway for bio‑inspired mechanical systems.