MUSAL · Multi-scale modelling of waves of porous media with applications to acoustic control and biomechanics

Multi-scale modelling of waves of porous media with applications to acoustic control and biomechanics

The aim of the project is to develop new models and methods to predict the dynamic properties and to describe the propagation of elastic waves in heterogeneous porous media. This subject is widely multidisciplinary and the results have applications in different areas of high economic, social and and humanitarian importance. The dynamic behaviour of heterogeneous media is characterised by a number of significant phenomena, such as phononic band gaps, negative refraction, dynamic anisotropy and wave focusing, acoustic diodes, acoustically invisible cloaks, wave localisation in structures with defects. These remarkable effects help to design new engineering devices in aerospace and automotive industries (acoustic absorbers, ultrasonic transducers and transmitters, lenses, wave guides, etc.) The modelling of wave propagation in heterogeneous media has great importance for non-destructive testing of materials and structures in mechanical and civil engineering. The pattern of phononic bands represents a kind of “identification portrait”, which is unique for every material. The larger frequency range explored, the more accurate “portrait” can be compiled. This gives a possibility to detect even very small variations of the microstructure and to develop new, more precise methods of acoustic diagnostic. In biomechanics, many live tissues (e.g., bones) can be modelled by porous media. Many people worldwide suffer from osteoporosis, a progressive bone disease that is characterized by a decrease in bone mass and density. Since osteoporosis itself has no symptoms, the detection of the bone structure using non-invasive testing is a challenge. The results of the project may ultimately be used for the early detection of the low bone density helping to stop the progress of osteoporosis by a prevention therapy. The study of wave propagation in porous media is also important for geological explorations. Understanding how the internal texture of soils and rocks affects the characteristics of travelling elastic waves helps to develop new robust methods for the detection of gas and oil reserves. The objectives of the project are as follows: 1. Development of new asymptotic methods to determine the dynamic properties of heterogeneous media. 2. Derivation of new homogenised models applicable in a wide range of frequencies. 3. Study of the propagation of elastic waves and determination of their dispersion properties. 4. Prediction of links between the properties of the microstructure and the characteristics of macroscopic waves. 5. Development of numerical procedures to verify the applicability of the proposed analytical approaches. 6. Clarification of phenomenological theories of wave propagation and suggesting new theoretical interpretations of their hypotheses.

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