Advertisement

Mathematical Aspects of Multi–Porosity Continua

  • Brian Straughan

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 38)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Brian Straughan
    Pages 1-34
  3. Brian Straughan
    Pages 35-48
  4. Brian Straughan
    Pages 49-70
  5. Brian Straughan
    Pages 71-95
  6. Brian Straughan
    Pages 97-110
  7. Brian Straughan
    Pages 111-130
  8. Brian Straughan
    Pages 153-164
  9. Brian Straughan
    Pages 165-173
  10. Brian Straughan
    Pages 175-189
  11. Back Matter
    Pages 191-208

About this book

Introduction

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.

Keywords

Double Porosity Triple Porosity Elasticity Continuous Dependence Waves Second Sound Continuum Mechanics Multi-Porosity Continua

Authors and affiliations

  • Brian Straughan
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DurhamDurhamUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-70172-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-70171-4
  • Online ISBN 978-3-319-70172-1
  • Series Print ISSN 1571-8689
  • Series Online ISSN 1876-9896
  • Buy this book on publisher's site