Composite Materials Mathematical Theory and Exact Relations

The mathematical method of composites has reached a very high level of maturity, and developments have increased our understanding of the relationship between the microstructure of composites and their macroscopic behaviour.

This book provides a self-contained unified approach to the mathematical foundation of the theory of composites, leading to the general theory of exact relations. It also provides complete lists of exact relations in many specific physically relevant contexts, such as conductivity, fibre-reinforced elasticity, piezoelectricity, thermoelectricity and more.

Divided into three parts, the book starts with a development of the mathematical theory of composites before progressing to the general theory of exact relationships and concludes with complete lists of exact relations. Written in a two-layer structure, each chapter starts with a non-technical review that is supported by deeper rigorous mathematical proof, this book will be key reading for graduate students and researchers involved with understanding and modelling composite materials. The extensive collection of explicit exact relations will also make it a useful reference for engineers to want to use composites to create materials with specific properties.