Inverse Design of Pre-Strain via a Predictive Electromechanical Model for Enhanced Strain Sensing

Pre-strain engineering is widely employed to enhance the sensitivity of flexible piezoresistive sensors, yet empirical pre-straining inevitably triggers severe trade-offs among sensitivity, linearity, hysteresis, and effective working range, leaving the identification of the optimal pre-strain an unresolved challenge. Here, an analytical electromechanical model rooted in microcrack evolution mechanics is developed that unifies two governing regimes - conductive-network fragmentation during initial loading and reversible crack opening-closure during steady-state cycling - reproducing experimental data with R² > 0.99 across eight pre-strain levels. Critically, all model parameters reduce to pre-strain-independent material constants, leaving strain and pre-strain as the only inputs; this separation extends the model from per-specimen fitting to a globally calibrated predictive framework that generates the complete electromechanical response at any untested pre-strain from only eight calibration datasets - a predictive capability absent from all prior microcrack circuit models. The predictive response surface is then coupled with multi-objective Pareto optimization to identify the optimal pre-strain. For smart-tire monitoring at 10% working strain, the inversely designed sensor (43.0% pre-strain) reduces median baseline drift from 8.52% to 1.93% (p = 1.19 × 10^{- 1 5}), and improves the signal-to-noise ratio (SNR) by 68.8% (p = 3.11 × 10^{- 1 1}) across 91 bench-test conditions.