Topology-informed design of intertwined architected materials: Unifying woven, knotted, and closed-chain networks

The design of architected materials with intertwined networks represents a promising avenue for creating structures with unique and programmable mechanical properties. However, a systematic, quantitative framework for prescribing and controlling the underlying fiber topology has remained elusive. This paper introduces a hierarchical computational framework that addresses this challenge by enabling the topology-informed design of intertwined helix-based architected materials and structures. The methodology progresses from an abstract, graph-based representation of port-level connectivity to the precise geometric realization of complex strand-level topologies with prescribed entanglement. We demonstrate the framework’s versatility by generating a wide array of intertwined networks, bridging woven, knotted, and closed-chain topologies, all unified under a single design paradigm. In addition, we present topological metrics that quantitatively capture the intertwining relationships among fibers—providing a valuable tool to map the prescribed design parameters to the resulting structural characteristics. Through a case study of a cubic lattice, we illustrate how the choice of port-level connectivity dictates material allocation and anisotropy, while the strand-level realization provides combinatorial freedom for tailoring specific entanglement patterns. This work establishes the foundation for designing intertwined architected materials, enabling control over topological invariants and providing a tool for exploring the influence of topology on material performance.