Small amplitude waves and stability for a pre-stressed viscoelastic solid

  • Michel Destrade
  • Ray W. Ogden
  • Giuseppe Saccomandi
Article

Abstract.

We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material of differential type. We use bulk waves and surface waves to address the questions of dissipation and of material and geometric stability. In particular, the analysis provides bounds on the constitutive parameters and on the predeformation that ensure linearized stability in the neighbourhood of a large pre-stretch. This type of result is relevant to the imaging of biological soft tissues using acoustical techniques, where pre-deformation is known to increase contrast and reduce de-correlation noise.

Mathematics Subject Classification (2000).

Primary 74J05 Secondary 74D10 

Keywords.

Nonlinear viscoelasticity prestressed materials material and geometric stability 

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Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  • Michel Destrade
    • 1
  • Ray W. Ogden
    • 2
  • Giuseppe Saccomandi
    • 3
  1. 1.Institut Jean Le Rond d’AlembertCNRS/Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Department of MathematicsUniversity of GlasgowGlasgowUK
  3. 3.Dipartimento di Ingegneria IndustrialeUniversità degli Studi di PerugiaPerugiaItaly

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