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