P. Letallec et C. Rahier, NUMERICAL-MODELS OF STEADY ROLLING FOR NONLINEAR VISCOELASTIC STRUCTURES IN FINITE DEFORMATIONS, International journal for numerical methods in engineering, 37(7), 1994, pp. 1159-1186
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.