Architecture-driven electromechanical behaviour and crack-based modelling of 3D printed multifunctional strain-sensing composites

Flexible and structurally integrated strain sensors fabricated through extrusion-based 3D printing have attracted increasing interest for structural health monitoring, wearable electronics, and soft robotic applications. However, relationships between printing architecture, sensing mechanisms, and electromechanical behaviour remain insufficiently established. In this study, co-extrusion 3D-printed continuous carbon fibre-reinforced polylactic acid (CF-PLA) and sequential dual-material Electrifi-thermoplastic polyurethane (Electrifi-TPU) sensors were comparatively investigated. Microscopy revealed distinct sensing mechanisms: CF-PLA exhibited resistance variation governed by intrinsic carbon fibre piezoresistivity and strain-dependent evolution of current-transfer pathways, whereas Electrifi-TPU was dominated by crack opening and conductive-network disruption. A unified crack-based analytical framework was developed and evaluated as a reduced-order representation of the electromechanical response of both sensing architectures. The non-through channel crack model showed the closest agreement with experimental relative resistance and gauge factor, with RMSE values of 0.014 for CF-PLA and 0.017 for Electrifi-TPU. The three-loop Electrifi-TPU sensor exhibited the highest sensitivity, reaching a gauge factor of 23.4 at 1.1% strain, while the three-loop CF-PLA sensor reached 15.9 at 0.8% strain with superior signal stability. Overall, this work presents a unified experimental–analytical framework that links fabrication– structure–property–sensing relationships, supporting the design and performance analysis of multifunctional 3D-printed strain sensors.