Zeitschrift für angewandte Mathematik und Physik

, Volume 63, Issue 6, pp 1143–1176 | Cite as

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



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.

Mathematics Subject Classification (2010)

74D10 Nonlinear constitutive equations 74F05 Thermal (mechanical-thermal) 74H10 Perturbations 74J05 Linear waves 


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


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringUniversity of Nebraska-LincolnLincolnUSA

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