We present sub-kpc-scale mapping of the 870 \mu m ALMA continuum emission in six luminous ( L _ { IR } ~ { } \sim~ { } 5 ~ { } \times 10 ^ { 12 } L _ { \odot } ) submillimeter galaxies ( SMGs ) from the ALESS survey of the Extended Chandra Deep Field South . Our high–fidelity 0.07 ^ { \prime \prime } -resolution imaging ( \sim 500 pc ) reveals robust evidence for structures with deconvolved sizes of \lesssim 0.5–1 kpc embedded within ( dominant ) exponential dust disks . The large-scale morphologies of the structures within some of the galaxies show clear curvature and/or clump-like structures bracketing elongated nuclear emission , suggestive of bars , star-forming rings , and spiral arms . In this interpretation , the ratio of the ‘ ring ’ and ‘ bar ’ radii ( 1.9 \pm 0.3 ) agrees with that measured for such features in local galaxies . These potential spiral/ring/bar structures would be consistent with the idea of tidal disturbances , with their detailed properties implying flat inner rotation curves and Toomre-unstable disks ( Q < 1 ) . The inferred one-dimensional velocity dispersions ( \sigma _ { r } \lesssim 70–160 km s ^ { -1 } ) are marginally consistent with the limits implied if the sizes of the largest structures are comparable to the Jeans length . We create maps of the star formation rate density ( \Sigma _ { SFR } ) on \sim 500 pc scales and show that the SMGs are able to sustain a given ( galaxy-averaged ) \Sigma _ { SFR } over much larger physical scales than local ( ultra– ) luminous infrared galaxies . However , on 500 pc scales , they do not exceed the Eddington limit set by radiation pressure on dust . If confirmed by kinematics , the potential presence of non-axisymmetric structures would provide a means for net angular momentum loss and efficient star formation , helping to explain the very high star formation rates measured in SMGs . Key words : galaxies : evolution – galaxies : formation – galaxies : starburst – galaxies : high-redshift – submillimeter : galaxies