Process optimization and density-modulus modeling for 3D-printed graded porous insoles

This is the authors' abstract. We don't add key points for this paper.

• Systematic optimization of MEX 3D printing parameters for TPE porous structures. • Established high-accuracy (R 2 >0.99) models linking elastic modulus to filling density for three lattice types. • Achieved high-fidelity manufacturing of graded porous insoles with <5% modulus deviation and <2% dimensional error. • The gyroid structure showed superior printability and a wide modulus range for functional gradient design. Functionally graded orthopedic insoles via MEX 3D printing face persistent challenges in achieving reliable modulus gradients, primarily due to poor interfacial bonding and the absence of quantitative density-modulus models for thermoplastic elastomer (TPE) lattices. To bridge this gap, this study establishes a comprehensive “process‑structure‑property” framework aimed at enabling precise and efficient manufacturing of graded porous insoles. Through orthogonal experiments, single‑factor tests, and two‑way ANOVA, key process parameters were optimized (layer thickness 0.2 mm, nozzle diameter 0.6 mm, speed 40 mm/s, temperature 230 °C), with the analysis revealing a significant interaction between layer thickness and temperature (p = 0.013). High‑fidelity cubic models (R² > 0.99) were developed that link filling density (10–50%) to compressive modulus (0.36–5.82 MPa) for square honeycomb, hexagonal honeycomb, and gyroid structures, among which the gyroid exhibited superior printability for graded interfaces. Fabricated insoles achieved <5% modulus deviation from predictions, <2% dimensional error, and a ∼12% reduction in peak plantar pressure as validated by finite‑element analysis. This work provides an engineer‑ready design library and a validated manufacturing pathway for biomechanically matched, personalized orthopedic devices.