Early-stage damage detection for buildings and bridges requires continuously sensing and assessing strain over large surfaces, yet with centimeter-scale resolution. To achieve this, we present a sensing sheet that combines high-performance ICs with exible electronics, allowing bonding to such surfaces. The exible electronics integrates thin-film strain gauges and amorphous-silicon control circuits, patterned on a polyimide sheet that can potentially span large areas. Non-contact links couple digital and analog signals to the ICs, allowing many ICs to be introduced via low-cost sheet lamination for energy-efficient readout and computation over a large number of sensors. Communication between distributed ICs is achieved by transceivers that exploit low-loss interconnects patterned on the polyimide sheet; the transceivers self-calibrate to the interconnect impedance to maximize transmit SNR. The system achieves multi-channel strain readout with sensitivity of 18μStrainRMS at an energy per measurement of 270nJ, while the communication energy is 12.8pJ/3.3pJ per bit (Tx/Rx) over 7.5m.