Viscoelastic Finite Element Formulation

Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

The finite element method is the most popular numerical procedure for the analysis of solids and structures, including those with time dependent properties. In this chapter, we present an incremental viscoelastic finite element formulation for problems with geometrical nonlinearity characterized by large displacements and rotations with small strains. The formulation is based on a total Lagrangian kinematic description. We begin with a brief presentation on the principle of virtual displacements for geometrically nonlinear problems. Procedures used for the computational implementation of the nonlinear viscoelastic model are also presented. We assume that the reader has a basic knowledge of the finite element method and of nonlinear continuum mechanics.

References

  1. 1.
    K.-J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice-Hall, Inc Englewood Cliffs, New Jersey, 1996)Google Scholar
  2. 2.
    M.A. Crisfield, Non-linear finite element analysis of solids and structures, vol. 1 (John Wiley & Sons Ltd, West Sussex, 2003)Google Scholar
  3. 3.
    S.P.C. Marques, G.J. Creus, Geometrically nonlinear finite elements analysis of viscoelastic composite materials under mechanical and hygrothermal loads. Comput. Struct. 53, 449–456 (1994)MATHCrossRefGoogle Scholar
  4. 4.
    B.F. Oliveira, G.J. Creus, Nonlinear viscoelastic analysis of thin-walled beams in composite material. Thin-Walled Struct. 41, 957–971 (2003)CrossRefGoogle Scholar
  5. 5.
    R.C. Pavan, B.F. Oliveira, S. Maghous, G.J. Creus, A model for anisotropic viscoelastic damage in composites. Compos. Struct. 92, 1223–1228 (2010)CrossRefGoogle Scholar
  6. 6.
    Y.B. Yang, M.S. Shieh, Solution method for nonlinear problems with multiple critical points. AIAA J. 28(12), 2110–2116 (1990)CrossRefGoogle Scholar
  7. 7.
    O.C. Zienkiewicz, R.L. Taylor, RL Finite Element Method for Solid and Structural Mechanics (Elsevier Butterworth-Heinemann, Jordan Hill, Oxford, 2005)Google Scholar

Copyright information

© The Authors 2012

Authors and Affiliations

  1. 1.Centro de TecnologiaUniversidade Federal de AlagoasMaceióBrazil
  2. 2.ILEAUniversidade Federal do Rio Grande do SulPorto AlegreBrazil

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