Propagation of infinitesimal thermo-mechanical waves during the finite-deformation loading of a viscoelastic material: General theory

Lili Zhang, Mehrdad Negahban

Research output: Contribution to journalArticle

Abstract

We study the theory of propagation of infinitesimal thermo-mechanical waves in a special class of nonlinear viscoelastic materials under homogeneous and inhomogeneous finite static and time-varying deformations. These results are based on a thermodynamically consistent finite-deformation nonlinear viscoelastic model that reduces to a general linear viscoelastic model of integral form. On a thermo-mechanically deforming body, we impose a thermo-mechanical perturbation history and obtain the equations to solve for the perturbation parameters from the constitutive model and the balance laws. We use these equations to study the characteristics of different perturbations. We develop the special equations for both time-harmonic and time-damping plane waves for homogeneous pre-loads.

Original languageEnglish (US)
Pages (from-to)1143-1176
Number of pages34
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume63
Issue number6
DOIs
StatePublished - Dec 1 2012

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Mechanical waves
Viscoelastic Material
Finite Deformation
Viscoelastic Model
Propagation
perturbation
propagation
Constitutive models
Perturbation
Balance Laws
Integral form
Damping
Parameter Perturbation
Constitutive Model
Plane Wave
Nonlinear Model
Linear Model
Time-varying
plane waves
Harmonic

Keywords

  • Anisotropy
  • Inhomogeneity
  • Integral model
  • Nonlinear viscoelasticity
  • Thermo-mechanical superposition
  • Thermo-mechanical wave
  • Wave propagation

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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abstract = "We study the theory of propagation of infinitesimal thermo-mechanical waves in a special class of nonlinear viscoelastic materials under homogeneous and inhomogeneous finite static and time-varying deformations. These results are based on a thermodynamically consistent finite-deformation nonlinear viscoelastic model that reduces to a general linear viscoelastic model of integral form. On a thermo-mechanically deforming body, we impose a thermo-mechanical perturbation history and obtain the equations to solve for the perturbation parameters from the constitutive model and the balance laws. We use these equations to study the characteristics of different perturbations. We develop the special equations for both time-harmonic and time-damping plane waves for homogeneous pre-loads.",
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