Abstract
This paper treats initial-boundary-value problems governing the motion in space of nonlinearly viscoelastic rods of strain-rate type. It introduces and exploits a set of physically natural constitutive hypotheses to prove that solutions exist for all time and depend continuously on the data. The equations are those for a very general properly invariant theory of rods that can suffer flexure, torsion, extension, and shear. In this theory, the contact forces and couples depend on strains measuring these effects and on the time derivatives of these strains.
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