More than half a century ago Penrose asked: are the superfluid and solid state of matter mutually exclusive or do there exist supersolid materials where the atoms form a regular lattice and simultaneously flow without friction? Recent experiments provide evidence that supersolid behavior indeed exists in Helium-4 -- the most quantum material known in Nature. In this paper we show that large local strain in the vicinity of crystalline defects is the origin of supersolidity in Helium-4. Although ideal crystals of Helium-4 are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system simply becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) undergoes a radical transformation and can become superfluid.
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