Vimentin coiled-coil alpha-helical dimers are elementary protein building blocks of intermediate filaments, an important component of the cell's cytoskeleton that has been shown to control the large-deformation behavior of eukaryotic cells. Here we use a combination of atomistic simulation and continuum theory to model tensile and bending deformation of single alpha-helices as well as coiled-coil double helices of the 2B segment of the vimentin dimer. We find that vimentin dimers can be extended to tensile strains up to 100% at forces below 50 pN, until strain hardening sets in with rapidly rising forces, approaching 8 nN at 200% strain. We systematically explore the differences between single alpha-helical structures and coiled-coil superhelical structures. Based on atomistic simulation, we discover a transition in deformation mechanism under varying pulling rates, resulting in different strength criteria for the unfolding force. Based on an extension of Bell's theory that describes the dependence of the mechanical unfolding force on the pulling rate, we develop a fully atomistically informed continuum model of the mechanical properties of vimentin coiled-coils that is capable of predicting its nanomechanical behavior over a wide range of deformation rates that include experimental conditions. This model enables us to describe the mechanics of cyclic stretching experiments, suggesting a hysteresis in the force-strain response, leading to energy dissipation as the protein undergoes repeated tensile loading. We find that the dissipated energy increases continuously with increasing pulling rate. Our atomistic and continuum results help to interpret experimental studies that have provided evidence for the significnificance of vimentin intermediate filaments for the large-deformation regime of eukaryotic cells. We conclude that vimentin dimers are superelastic, highly dissipative protein assemblies.