Final Report Summary - BIOSMA (Mathematics for Shape Memory Technologies in Biomechanics)
Shape memory alloys (SMAs) are active materials: remarkably large deformations can be induced by either thermal, mechanical, or magnetic stimuli. This amazing material behavior is at the basis of a variety of innovative applications ranging to sensing and actuators, to seismic and aerospace technologies, just to mention a few hot topics. In particular, SMAs are nowadays widely exploited within biomedical applications in orthodontics, orthopedics, medical instruments and minimal invasive surgery, drug delivery systems. Among the most relevant biomedical applications of SMAs are stents for intra-vascular or extra-vascular scaffolding.
The BioSMA project is focused on an interdisciplinary research program toward the development and integration of efficient and reliable mathematical tools for the modeling and the simulation of SMAs devices. Thermo-mechanical three-dimensional evolution models for SMAs are generally described by systems of partial differential equations and variational inequalities of thermoelastic and phase-transition type. The mathematical and numerical treatment of these systems is very challenging and requires accurate analytical and functional techniques. The BioSMA activity is especially directed to confront with the many interesting and crucial materials features of the macroscopic behavior of SMAs that still need to receive consideration in connection with Biomechanical applications. In particular, the project is aimed at considering both isothermal and thermally-coupled systems, describing the effect of training and fatigue in SMAs, and model the ferromagnetic shape-memory effect.
The BioSMA research team, often in collaboration with other international groups, has worked in all of these directions. We have introduced new modeling ideas and developed the relevant analysis of the corresponding mathematical problems. The research has produced new descriptions of the behavior of the materials and the relevance of training aspects. We have investigated the the full thermo-mechanical coupling problem and initiated the study of thermal control. Moreover, a novel modelization of the ferromagnetic shape-memory effect has been advanced and the respective mathematical theory has been specified.
The BioSMA project is focused on an interdisciplinary research program toward the development and integration of efficient and reliable mathematical tools for the modeling and the simulation of SMAs devices. Thermo-mechanical three-dimensional evolution models for SMAs are generally described by systems of partial differential equations and variational inequalities of thermoelastic and phase-transition type. The mathematical and numerical treatment of these systems is very challenging and requires accurate analytical and functional techniques. The BioSMA activity is especially directed to confront with the many interesting and crucial materials features of the macroscopic behavior of SMAs that still need to receive consideration in connection with Biomechanical applications. In particular, the project is aimed at considering both isothermal and thermally-coupled systems, describing the effect of training and fatigue in SMAs, and model the ferromagnetic shape-memory effect.
The BioSMA research team, often in collaboration with other international groups, has worked in all of these directions. We have introduced new modeling ideas and developed the relevant analysis of the corresponding mathematical problems. The research has produced new descriptions of the behavior of the materials and the relevance of training aspects. We have investigated the the full thermo-mechanical coupling problem and initiated the study of thermal control. Moreover, a novel modelization of the ferromagnetic shape-memory effect has been advanced and the respective mathematical theory has been specified.