Time domain modeling of damping using anelastic displacement fields and fractional calculus

Mikael Enelund, George A. Lesieutre

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


A fractional derivative model of linear viscoelasticity based on the decomposition of the displacement field into an anelastic part and elastic part is developed. The evolution equation for the anelastic part is then a differential equation of fractional order in time. By using a fractional order evolution equation for the anelastic strain the present model becomes very flexible for describing the weak frequency dependence of damping characteristics. To illustrate the modeling capability, the model parameters are fit to available frequency domain data for a high damping polymer. By studying the relaxation modulus and the relaxation spectrum the material parameters of the present viscoelastic model are given physical meaning. The use of this viscoelastic model in structural modeling is discussed and the corresponding finite element equations are outlined, including the treatment of boundary conditions. The anelastic displacement field is mathematically coupled to the total displacement field through a convolution integral with a kernel of Mittag-Leffler function type. Finally a time step algorithm for solving the finite element equations are developed and some numerical examples are presented.

Original languageEnglish (US)
Pages (from-to)4447-4472
Number of pages26
JournalInternational Journal of Solids and Structures
Issue number29
StatePublished - May 12 1999

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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