The Frank-Read (F-R) source, a well-studied concept in metallurgy, is a mechanism by which dislocation loops are emitted via repeated heterogeneous nucleation, giving rise to ductility in crystalline solids. We demonstrate that the same fundamental mechanism enables multiplication of disclination loops in nematic liquid crystals under shear. And while F-R sources form randomly in deformed crystals e.g. through dislocation pinning by impurities, by contrast we can precisely engineer F-R sources in a nematic liquid crystal cell by inscribing anchoring patterns on the confining substrates. We discuss possible applications in passive and active nematics.