Mathematical tools for shape memory alloys
Mathematically, SMA systems are very complex and requires a high degree of accuracy when using analytical and functional techniques. An interdisciplinary research team worked together in the BIOSMA (Mathematics for shape memory technologies in biomechanics) project to develop accurate mathematical tools. They studied SMA properties as well as behaviour in response to thermal, mechanical, or magnetic stimuli. BIOSMA members focused on isothermal and thermally-coupled systems to determine the macroscopic behaviour of SMAs and assess the training, fatigue and ferromagnetic shape-memory effect. They also formed collaborations with international research groups to work on these aspects. Researchers met with considerable success and introduced new modelling ideas and produced novel SMA behaviour descriptions. Besides investigating the full thermo-mechanical coupling problem, they also initiated the study of thermal control. A key accomplishment is the modelisation of ferromagnetic shape-memory effect and the corresponding mathematical theory. Some interesting applications addressed include the feasibility assessment of SMAs in designing seismic isolation systems as well as the design of micro-actuators. The potential applications of SMAs in biomedicine alone are innumerable as they are suitable for use in orthopaedic implants, drug delivery, invasive surgery as well as intra-vascular stents. Other applications include incorporation into sensors and actuators for seismic and aerospace technologies. Project activities have laid the groundwork for developing accurate and reliable macroscopic modelling tools to determine SMA properties and design innovative SMA-based devices. This should aid in the resolution of real-scale biomechanical engineering problems for optimisation of SMA production processes.
Keywords
Mathematical, shape memory alloy, isothermal, thermally-coupled, macroscopic behaviour, fatigue, ferromagnetic shape-memory, modelling, seismic isolation, micro-actuator, stent, sensor
