  In a crystalline solid under mechanical stress, a Frank-Read source is a
pinned dislocation segment that repeatedly bows and detaches, generating
concentric dislocation loops. We demonstrate that in nematic liquid crystals,
an analogous Frank-Read mechanism can generate concentric disclination loops.
Using experiment, simulation, and theory, we study a disclination segment
pinned between surface defects on one substrate in a nematic cell. Under
applied twist of the nematic director, the pinned segment bows and emits a new
disclination loop which expands, leaving the original segment intact; loop
emission repeats for each additional 180$^\circ$ of applied twist. We present
experimental micrographs showing loop expansion and snap-off, numerical
simulations of loop emission under both quasistatic and dynamic loading, and
theoretical analysis considering both free energy minimization and the balance
of competing forces. We find that the critical stress for disclination loop
emission scales as the inverse of segment length, and changes as a function of
strain rate and temperature, in close analogy to the Frank-Read source
mechanism in crystals. Lastly, we discuss how Frank-Read sources could be used
to modify microstructural evolution in both passive and active nematics.
