Deuteron-nucleus elastic scattering at intermediate energies is analysed using a deuteron interaction obtained from the covariant folding of recent energy- and atomic-mass-number-dependent global Dirac-phenomenology nucleon-nucleus potentials. The effects of allowing the nucleons in the deuteron to interact with the target with a variable energy, determined by their relative momentum, are studied for the first time. The inclusion of these effects in parameter-free calculations of cross section and polarization observables for deuteron elastic scattering on ²⁴Mg, ⁴⁰Ca and ⁵⁸Ni improves the agreement with the data at deuteron energies of 400 and 700 MeV and is particularly strong at 400 MeV.