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Numerical models of steady rolling for non‐linear viscoelastic structures in finite deformations
Author(s) -
Le Tallec P.,
Rahler C.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620370705
Subject(s) - viscoelasticity , constitutive equation , finite element method , rotational symmetry , conservation law , mathematics , continuum mechanics , classical mechanics , lagrangian and eulerian specification of the flow field , mechanics , mathematical analysis , lagrangian , physics , geometry , thermodynamics , eulerian path
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.