Numerical models of steady rolling for non‐linear viscoelastic structures in finite deformations

A Lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented. These laws are expressed by a non‐linear differential equation governing the evolution of an internal variable. Then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics. A finite element approximation and a solution technique of the algebraic system is proposed. The eiimination of the internal variable allows one to keep an elastic‐like algorithm with an independent solution of the viscoelastic equation. Numerical tests show the feasibility and the efficiency of the proposed methods in large three‐dimensional situations.