A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS

Abstract

We present a Cosserat-based three-dimensional to one-dimensional reduction in the case of a thin rod, of the viscoelastic finite strain model introduced by Neff. This model is a coupled minimization/evolution problem. We prove the existence and uniqueness of the solution of the reduced minimization problem. We also show a few regularity results for this solution which allow us to establish the well-posedness of the evolution problem. Finally, the reduced model preserves observer invariance.