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Small amplitude waves and stability for a pre-stressed viscoelastic solid. (English) Zbl 1169.74024

Summary: 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 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.

MSC:

74J10 Bulk waves in solid mechanics
74J15 Surface waves in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
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