Mini-Workshop: The Mathematics of Electro-Active Smart Materials
Authors: Dorfmann Luis , Ogden Ray W. , Saccomandi Giuseppe 
Published: December 2009

The mini-workshop
The Mathematics of Electro-Active Smart Materials
, was attended by 15 participants (7 from Europe, 4 from USA and 1 from Israel). This workshop contained a nice blend of researchers with various backgrounds: mathematics, physics, engineering science and chemistry. The interdisciplinarity of the invited participants was essential because smart materials, such as piezoceramics, magnetostrictives and electroactive polymers, are characterized by strong couplings between their mechanical properties and applied electric, magnetic or thermal fields. Therefore skills in several areas of science are needed to understand the complicated and highly nonlinear behavior of such materials.

Science and technology have produced amazing developments in the design of electronics and machinery using smart materials. Some everyday items are already incorporating smart materials (cars, the International Space Station, eyeglasses, coffee pots, speakers, for example) and the number of applications is growing steadily. For example, electro-rheological (ER) and magneto-rheological (MR) materials are fluids that can experience a dramatic change in their viscosity. They can change from a thick fluid (similar to motor oil) to nearly solid substances within the span of a millisecond when exposed to a magnetic or electric field; the effect can be completely reversed just as quickly when the field is removed. MR fluids are being developed for use in car shock absorbers, damping of machine vibration, prosthetic limbs, exercise equipment, and surface polishing of machine parts, in particular. ER fluids have been developed mainly for use in clutches and valves, as well as in engine mounts where they are designed to reduce noise and vibration in vehicles. More recently, magneto- and electro-sensitive elastomers have been developed and commercialized. Such materials are capable of large elastic deformations and a rapid and significant change in their material properties on the application of a magnetic or electric field. The coupling in the material response is achieved and optimized by distributing within an elastomeric matrix micron size ferrous particles. Cross-linking may occur, for example, in the presence of an applied field, whereby particles form chain-like structures aligned along the applied field direction. The material is then characterized by two families of preferred direction and may result in highly controllable smart materials.
Mathematical and computational methods pervade research, development, testing, and evaluation problems encountered by researchers in the field of smart materials. Furthermore, increasing demands are being placed on research in the mathematical sciences because of their fundamental roles in the analysis and modelling issues that arise in such complex materials.
In this Mini-Workshop we have discussed recent mathematical and computational questions related to the modelling of smart materials used in structures, actuators and sensors from the point of view of material properties and control of mechanical properties.
The first talk by G. A. Maugin was on overview of existing theories capable of describing the strong coupling between mechanical properties and applied fields in electro- and magneto-active smart materials. This overview was extremely interesting also because it was punctuated with historical notes and remarks.
On the other hand M. Zrinyi gave an exhaustive review of the phenomenology of such materials and of experimental data. This was extremely useful for facilitating a clear identification of further key experiments that should be conducted in order to provide more comprehensive data for improving the modelling process.
The other talks have been devoted to