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Composite materials are heterogeneous by nature, and are intended to be, since only the combination of different constituent materials can give them the desired combination of low weight, stiffness and strength.
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale.
1.1 What are composites, and why study them? 1 1.2 What makes composites useful? 2 1.3 The effective tensors of composites 5 1.4 Homogenization from an intuitive viewpoint 7 1.5 Periodic homogenization 8 1.6 Homogenization in random media 11 1.7 Homogenization in the settings of G-, H-, and 0-convergence 12 References 14
Introduction. Mechanical properties of composites depends on the volume fraction of reinforcement and matrix. The basic properties can be calculated using rule-of-mixture principle with some assumptions. The type of reinforcement (fiber, particle or whiskers) and their orientation play a major role in determining the strength of composites.
It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers.
Topics in the Mathematical Modelling of Composite Materials. Book. © 2018. Download book PDF. Overview. Editors: Andrej V. Cherkaev, Robert Kohn. Demonstrates interdisciplinary work in many physical problems involving optimal design, composite materials, and coherent phase transitions.
Introduction. Displacements, Strains, and Stresses. 2.1 Strain–Displacement Relations. 2.2 Equilibrium Equations. 2.3 Stress-Strain Relationships.
