  Lattice reconstruction and corresponding strain accumulation play a key role
in defining the electronic structure of two-dimensional moir\'e superlattices,
including those of transition metal dichalcogenides (TMDs). Imaging of TMD
moir\'es has so far provided a qualitative understanding of this relaxation
process in terms of interlayer stacking energy, while models of the underlying
deformation mechanisms have relied on simulations. Here, we use interferometric
four-dimensional scanning transmission electron microscopy to quantitatively
map the mechanical deformations through which reconstruction occurs in
small-angle twisted bilayer MoS2 and WSe2/MoS2 heterobilayers. We provide
direct evidence that local rotations govern relaxation for twisted
homobilayers, while local dilations are prominent in heterobilayers possessing
a sufficiently large lattice mismatch. Encapsulation of the moir\'e layers in
hBN further localizes and enhances these in-plane reconstruction pathways,
suppressing out-of-plane corrugation. We also find that extrinsic uniaxial
heterostrain, which introduces a lattice constant difference in twisted
homobilayers, leads to accumulation and redistribution of reconstruction
strain, demonstrating another route to modify the moir\'e potential.
