Publisher's Synopsis
The mathematical theory of composite materials is a branch of mechanics that deals with the analysis and modelling of materials composed of two or more distinct constituents. Overall, the mathematical theory of composite materials aims to provide a framework for understanding and predicting the mechanical behaviour of composite structures. It enables engineers and researchers to design and optimize composite materials for specific applications, considering factors such as load-bearing capacity, stiffness, strength, and durability.
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. 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.
This extended and updated new edition captures developments and results since the original edition and includes new chapters on thermoelasticity, a combination of elasticity and heat conduction theories and defines the response of the material to changes in pressure and temperature, and thermoelectricity , which concerns itself with temperature driven changes to electrical properties. Key topics requires to define the applicability of certain materials.
Key Features:
- Homogenization theory for composite media developed in a novel unified framework covering many physical contexts, such as conductivity, elasticity, piezoelectricity, etc.
- Has complete lists of exact relations and links in all physically relevant contexts
- Can be used by practitioners, who are not mathematicians by consulting Part III of the book written with such an audience in mind
- Would be of interest to broader community of mathematician in the area of Calculus of Variations
