The influence of nonlinear pre-stress on wave propagation through viscoelastic composites.

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Visco-elastomeric (VE) materials which are inhomogeneous (i.e. their material properties are spatially dependent) are employed in numerous applications within the industrial sector, e.g. noise and vibration isolators in machinery and the automotive and aerospace industry, bridge bearings and seismic shock absorbers in civil engineering applications and acoustic tiles used on underwater vehicles, the latter being the example of specific interest in this project. They also arise naturally as soft biological tissues in the body. In these contexts the materials are frequently subjected to pressures which lead to large deformations (i.e. a nonlinear pre-stress) of the material. In the underwater vehicle context, viscoelastic acoustic tiles are subjected to massive compressional forces as the vehicle dives leading to a large deformation of the material. In the soft tissue context, a pre-stress may exist due to some existing residual stress or it could be induced by physiological or mechanical mechanisms, e.g. for medical purposes, in order to increase tissue contrast before scans. The subsequent incremental (linear) response of VE materials can be of great use with regard to the stability, incremental constitutive behaviour or simply the fitness-for-purpose of the materials in question. The behaviour of composite materials can be assessed in these nonlinear pre-stressed states by using non-destructive evaluation (NDE) techniques, e.g. sending ultrasonic waves through the media and measuring the response. In the soft-tissue context the incremental wave would be the imaging tool for diagnosis.Various aspects of pre-stress in homogeneous materials and simple inhomogeneous materials have been assessed previously but the more difficult problem of generally inhomogeneous materials has not been described fully in the literature. This collaborative project, between the School of Mathematics in Manchester and Thales Underwater Systems Ltd (TUSL), aims to develop a general theory in order to describe the influence of nonlinear pre-stress on wave propagation through inhomogeneous media. This theory will then be applied in order to predict the constitutive response of particulate composites of interest to TUSL, although the general theory will be applicable to many inhomogeneous structures.