An Introduction to the Mathematical Theory of Dynamic Materials (Hardcover) (ISBN-13: 9780387382784)

This book describes a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials---material substances whose properties are variable in space and time. The book discusses some general features of dynamic materials as thermodynamically open systems; it gives their adequate tensor description in the context of Maxwell's theory of moving dielectrics and makes a special emphasis on the theoretical analysis of spatio-temporal material composites (such as laminates and checkerboard structures). Some unusual applications are listed along with the discussion of some typical optimization problems in space-time via dynamic materials. This book will interest applied mathematicians interested in optimal problems of material design for systems governed by hyperbolic differential equations; researchers in the field of smart metamaterials and their applications to optimal material design in dynamics.