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

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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-dam** plane waves for homogeneous pre-loads.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, USA

    Lili Zhang & Mehrdad Negahban

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  1. Lili Zhang
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  2. Mehrdad Negahban
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Correspondence to Mehrdad Negahban.

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Zhang, L., Negahban, M. Propagation of infinitesimal thermo-mechanical waves during the finite-deformation loading of a viscoelastic material: general theory. Z. Angew. Math. Phys. 63, 1143–1176 (2012). https://doi.org/10.1007/s00033-012-0200-5

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  • DOI: https://doi.org/10.1007/s00033-012-0200-5

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