Multi-response optimization of 3D printed kirigami designs for enhancing flexible strain sensors

Kirigami-based structures have emerged as a promising approach for enhancing the stretchability and sensitivity of flexible strain sensors. However, their fabrication using fused deposition modeling (FDM) remains challenging due to limitations in dimensional accuracy and process variability. In particular, the relationship between kirigami geometric design parameters and sensor performance has not been systematically quantified. This study presents a multi-response optimization of FDM-fabricated kirigami strain sensors using conductive thermoplastic polyurethane (TPU). Three kirigami patterns with distinct slit configurations (Patterns A–C), along with slit ratio, thickness, and substrate type, were investigated using Response Surface Methodology (RSM) with an I-optimal design. The responses included build time, dimensional deviation, gauge factor (GF), and elongation. The optimized configuration achieved a build time of 2.07 min, a dimensional deviation of 1.81%, a gauge factor of 18.10, and an elongation of 126.38%. Validation experiments showed strong agreement between predicted and experimental results, with errors below 5.62% for all responses. The results reveal that kirigami geometry governs strain localization and sensitivity, while thickness and substrate influence manufacturability and mechanical robustness. The proposed framework provides a systematic approach for balancing sensing performance and fabrication constraints in additively manufactured flexible sensors.