NUMERICAL-MODELS OF STEADY ROLLING FOR NONLINEAR VISCOELASTIC STRUCTURES IN FINITE DEFORMATIONS

A Lagrangian formulation of constitutive laws for a viscoelastic mater ial based on irreversible thermodynamics is first presented. These law s are expressed by a non-linear differential equation governing the ev olution of an internal variable. Then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from th e conservation laws of continuum mechanics. A finite element approxima tion and a solution technique of the algebraic system is proposed. The elimination of the internal variable allows one to keep an elastic-li ke algorithm with an independent solution of the viscoelastic equation . Numerical tests show the feasibility and the efficiency of the propo sed methods in large three-dimensional situations.