Topological optimization of heterogeneous strain structures for computational design of ultra-sensitive strain sensors

Heterogeneous strain engineering offers a promising approach for developing high-performance stretchable strain sensors, but the optimal strain distributions remain unexplored. Herein, we derive the optimal strain topology for achieving maximum sensitivities using Monte Carlo simulations, and identify the key sensitivity-regulating parameters, thus establishing a general computational design guideline. Mathematical analysis demonstrates that within the optimal topology, sensitivity is maximized by reducing the strain value of low-strain regions or increasing their area proportion. As proof of concept, patterned graphene strain sensors (PGSSs) featuring parameterized grooves are designed with their small strain values and proportions precisely modulated via finite element analysis. Adjusting these parameters enhances sensitivity by factors of ~10.7 and 3.3, with the highest gauge factor reaching 25,600 at 100% strain. Furthermore, the PGSSs can effectively detect human body motions and gauge object dimensions when integrated with robot grippers. The computational framework exhibits applicability across different heterogeneous strain engineering methods.