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

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.

Direct beneficiaries of the proposed project are Thales Underwater Systems Ltd (TUSL). Results will be implemented into their computer codes in order to improve current materials models. The proposed project is part of the next wave of scientific research into materials design for submarines and will inform the decision-making process for the use of such materials in future submarines and sonar equipment. Improvements made in this design process will therefore aid UK PLC substantially by impacting upon and improving the materials aspect of this design plan. More generally the theory developed within this research project is applicable to generally inhomogeneous materials. The many uses of these structures are outlined in the Case for Support and therefore wider communities can certainly benefit from this research. In particular we stress the potential applicability to, and impact in health-care, including soft tissue modelling and imaging science. Several personnel will work on aspects within this research proposal, ranging from summer Undergraduate students to a 3-year Postdoctoral Research Assistant. All of these personnel will benefit from numerous aspects of the project; these benefits will include secondment time spent within the project partner organization and development of team-work and communication (both written and oral) skills. They will be also given opportunites to improve such skills by attendance at University run courses. The project will be managed by the PI with assistance from the CI. Internal communication between the project team at Manchester will be achieved via weekly team meetings, allowing progress to be monitored and guidance to be given. As regards communication with TUSL, the PI and CI have had many successful collaborations with TUSL, having excellent existing lines of communication at all levels within the organization. Informal meetings with TUSL will take place every two months with formal meetings planned every 6 months. Every member of the team will attend these; the PDRA and PhD student will give talks on their progress within the project at formal meetings, permitting dissemination of the research as it happens. The meetings will also allow guidance from TUSL to ensure that the aims and objectives of the project are met. The proposed project will significantly improve the existing links between the School of Mathematics at Manchester and TUSL. Indeed it is an exciting time for this collaboration since the proposed project will lead to a significant research team being based within the School. A workshop dedicated to waves in pre-stressed media will be organized during the project, enabling dissemination of the proposed research whilst interacting with the specific community of academics and industrialists interested in this area. Communication with the wider academic and industrial community will be achieved by talks given at national and international conferences throughout the project. The PI and CI's links with researchers at several other industrial organizations can also engage the wider industrial community in the research. Exploitation of results derived during the project, and especially those which will have most impact, will be straightforward due to the constant communication between the School of Mathematics and TUSL. Secondments of project members to TUSL will also enable this to happen easily since seconded staff can spend time with researchers on a one-to-one basis at TUSL. During these secondments, computational models can be adapted and modified. New codes can also be written when required with the input of the team members. Researchers at TUSL will write such codes but the input of the secondment staff will be imperative. Finally, we note that collaborative agreements for PhD CASE studentships have been drawn up in the past between TUSL and the University of Manchester. No problems have arisen and we envisage a similar situation with this project.