Overview
- Presents new analyses of nonlinear waves
- Examples provided at the end of every chapter
- Provides new models, including second sound
- Includes an extensive bibliography
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 38)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.
Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion.This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.
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Bibliographic Information
Book Title: Mathematical Aspects of Multi–Porosity Continua
Authors: Brian Straughan
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-319-70172-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-70171-4Published: 02 December 2017
Softcover ISBN: 978-3-319-88895-8Published: 04 September 2018
eBook ISBN: 978-3-319-70172-1Published: 30 November 2017
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: IX, 208
Number of Illustrations: 3 b/w illustrations, 4 illustrations in colour
Topics: Computational Science and Engineering, Solid Mechanics, Mathematical Applications in the Physical Sciences