  We present sub-kpc-scale mapping of the 870 $\mu$m ALMA continuum emission in
six luminous ($L_{\rm IR}~\sim~5~\times10^{12}$ L$_{\odot}$) submillimeter
galaxies (SMGs) from the ALESS survey of the Extended Chandra Deep Field South.
Our high-fidelity 0.07$''$-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_{\rm 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 ($\Sigma_{\rm SFR}$) on $\sim$500 pc scales and
show that the SMGs are able to sustain a given (galaxy-averaged) $\Sigma_{\rm
SFR}$ 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.
