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Monitoring fatigue cracking of large engineering structures is a costly and time-intensive process. The authors' present the first low-cost inkjet-printed patch antenna sensor that can passively detect crack formation, orientation and shape by means of resonant frequency shifts in the two resonant modes of the antenna. For the first time, the effect of non-linear crack shapes on the parallel and perpendicular resonant modes of a patch antenna is quantified with simulation and measurement. This study presents a step towards fully integrated, low-cost, conformal and environmentally friendly smart skins for real-time monitoring of large structures.