One of the primary interest areas in the burgeoning field of material science is the study of smart material systems. Smart material systems have been in vogue since the 1960s, but interest in them has grown tremendously since the beginning of the 1990s, in large part due to applications in aerospace, aeronautics, industry, sensor networks, automotive systems, biomedical applications, space technologies, and even common devices such as exercise machines.

Some examples can be noted: transducers are devices that use smart materials that generate electric, magnetic, or thermal fields in response to physical stresses (or that generate physical stresses in response to such fields). These may be used as actuators, where electrical energy is converted into mechanical form, or as sensors, where mechanical energy is converted into electrical form. Shape memory alloys are used in places where an artifact or component has the property of returning to a desired physical shape after a transient deformative impulse is removed, usually upon application of heat.

This book is devoted to a brief description of various types of smart material systems, along with detailed descriptions of the mathematical models that are applicable to them. The first chapter begins with a general introduction to smart material applications, and introduces the types that are later considered in the book. The subsequent four chapters have a common format: the physical properties of the materials under consideration in each are briefly introduced, and then the various mathematical models that relate to them (as given in the research literature) are stated in some detail. The second chapter addresses ferroelectric compounds, the third discusses relaxor ferroelectric compounds, the fourth covers ferromagnetic compounds, and the fifth explains shape memory alloys. The sixth chapter presents the models that attempt to provide a unified framework to describe ferroic compounds. The seventh chapter discusses models for rods, beams, plates, and shells, with a particular focus on these structures constructed out of smart materials. The eighth and final chapter discusses numerical methods for use with the structural models for rods, plates, and so on.

The book assumes, as might be expected, a significant background and depth in its subject, and probably would not be of use to those who are not well versed in nonlinear mathematics, differential equations, functional analysis, and such areas that are not normally encountered in adequate depth outside of graduate mathematics courses. The book would be a handy reference for people who need to look up something concerning the mathematics of smart material systems, but would probably not be easy to use as a textbook in a regular course, even at the graduate level. The included topic index is helpful, but there are no student exercises, and the appendices that give a brief outline of some of the needed mathematical background are evidently not meant to be comprehensive indicators of that background.