Design and Characterization of Negative-Stiffness Lattice Structures for Diabetic Midsoles

Featured Application Negative-stiffness lattice structures represent a groundbreaking class of mechanical metamaterials capable of redistributing pressure in highly efficient and adaptive ways. Thanks to their unique ability to undergo localized deformation while maintaining global structural integrity, these lattices are ideal for applications requiring uniform load distribution, energy absorption, and enhanced comfort. From biomedical implants to aerospace panels and protective equipment, their tunable mechanical response opens new frontiers in design and performance.Abstract Diabetes mellitus often leads to peripheral neuropathy that compromises protective sensation in the feet and raises ulcer risk through mechanical overload. While prior research has introduced cellular-metamaterial-based shoe midsoles for dynamic plantar pressure redistribution, this study advances the field by delivering a complete, application-oriented workflow for physical prototyping and mechanical validation of such structures. Our pipeline integrates analytical synthesis of curved-beam unit cells, process calibration, and fabrication via thermoplastic polyurethane (TPU) fused-filament fabrication, producing customized, test-ready lattices suitable for future gait-simulation studies and in vivo assessment. Printed TPU tests showed a Young's modulus of 44.5 MPa, ultimate tensile strength of 4.9 MPa, and strain at break approximate to 20% (Shore 84.5 A/37.2 D). The cellular unit's compressive response was quantified by theoretical force-threshold estimates and controlled compression tests, enabling data-driven selection of unit cell geometry and arrangement for effective offloading. The response is rate-dependent: higher loading speed increases peak force and hysteresis, indicating that loading rate should be treated as a design parameter to tune dynamic behavior for the target application. Although the analytical model overestimates forces by roughly 50% on average relative to experiments, it accurately captures the influence of key geometric parameters on peak force. Accordingly, experimental data can identify cell strategic geometric parameters (i.e., Q), while the achievable maximum force can be predicted from the model by applying an appropriate correction factor. By connecting modeling, calibration, and experimental validation in one coherent path, the proposed workflow enables manufacturable lattices with controllable activation thresholds for plantar pressure redistribution and provides a practical bridge from concept to application.