Biological systems often employ disordered, or stochastic, architectures to achieve an exceptional balance between mechanical properties, density, and efficient transport. For instance, the random network of “struts” in living tissues such as trabecular bone or coral skeletons not only distributes mechanical loads effectively but also facilitates fluid flow for nutrient transport to sustain life. However, the design and fabrication of these structures with high fidelity across practical length scales for deep analysis of engineering applications remains a non-trivial matter. In this work, we present a new approach that leverages topological defect networks emerging from the self-assembly of chiral liquid crystals as a platform for designing disordered architectures. Chiral nematic liquid crystals, defined by their long-range orientational order of rod-like molecules arranged in a twisted pattern, exhibit distinct phase behaviors governed by a balance of elastic interactions, externally induced fields, and topological constraints. In highly chiral systems, the liquid crystal molecules self-assemble into double-twisted cylinder (DTC) mesostructures, stabilized by complex disclination (defect) networks that can exhibit both ordered and disordered characteristics. In this study, we simulate textures formed by stochastically initialized disclination networks, which give rise to an amorphous assembly of DTCs. This results in a continuous, interconnected curvilinear disclination network. Using a Landau–de Gennes framework , we develop phase field models describing the long-range spatial distribution of orientational ordering of chiral nematic liquid crystal molecules. Interestingly, subsequent thresholding of the scalar order parameter, a key value in determining local orientation, reveals bicontinuous architectures reminiscent of trabecular bone. By adjusting several key thermodynamic system parameters (thermal conditions, chirality, elastic constants) of our LdG guided simulations, we can effectively “fine tune” structural characteristics with respect to changes in the system conditions. Next, we employ statistical image analysis (via ImageJ plugins) and differential geometry to extract key structural features (ligament diameters, surface curvature, relative density, connectivity) to characterize various realizations and map their features to the simulation input parameters. Virtual realizations are extracted and assessed via Finite Element Analysis to correlate these microstructural features with their predicted effective elastomechanical responses. Finally, we scale and fabricate statistically representative architectures using Stereolithography 3D printing to examine how their unique nano-structural features influence continuum-level mechanical performance at higher (sub-millimeter feature size) length scales, thereby validating our numerical predictions. Our work establishes a fundamental understanding of structure–mechanics relationships in disordered porous materials, further advancing the development of bioinspired architectures for lightweight, load-bearing applications.
