Wave propagation in pre-stressed nonlinear inhomogeneous media

Dr. Will Parnell (University of Manchester)

Thursday 24th March, 2011 14:00-15:00 325


The influence of nonlinear pre-stress on subsequent small-amplitude wave propagation through homogeneous media has been well studied in the literature, particularly for cases when the initial pre-stress is homogeneous. In this case the wave can be considered to be propagating through a material with induced anisotropy, but with an elastic modulus tensor that is spatially homogeneous. In many important cases however, the initial pre-stress will not lead to a deformation field that is homogeneous. The subsequent small-amplitude deformation is then governed by a pde with spatially dependent coefficients. In the case of a composite material, these coefficients also vary rapidly. This case has not been considered in-depth in the literature. Here we consider several problems relating to inhomogeneous deformations and subsequent linear wave propagation. In particular we relate results to applications in composites and "tunable" smart materials.

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