Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Some Elements of Continuum Mechanics
- 3 Motivation for Seeking a Molecular Scale-Dependent Perspective on Continuum Modelling
- 4 Spatial Localisation, Mass Conservation, and Boundaries
- 5 Motions, Material Points, and Linear Momentum Balance
- 6 Balance of Energy
- 7 Fine-Scale Considerations: Moments, Couple Stress, Inhomogeneity, and Energetics
- 8 Time Averaging and Systems with Changing Material Content
- 9 Elements of Mixture Theory
- 10 Fluid Flow through Porous Media
- 11 Linkage of Microscopic and Macroscopic Descriptions of Material Behaviour via Cellular Averaging
- 12 Modelling the Behaviour of Specific Materials: Constitutive Relations and Objectivity
- 13 Comments on Non-Local Balance Relations
- 14 Elements of Classical Statistical Mechanics
- 15 Summary and Suggestions for Further Study
- Appendix A Vectors, Vector Spaces, and Linear Algebra
- Appendix B Calculus in Euclidean Point Space ℰ
- References
- Index
Preface
Published online by Cambridge University Press: 05 November 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Some Elements of Continuum Mechanics
- 3 Motivation for Seeking a Molecular Scale-Dependent Perspective on Continuum Modelling
- 4 Spatial Localisation, Mass Conservation, and Boundaries
- 5 Motions, Material Points, and Linear Momentum Balance
- 6 Balance of Energy
- 7 Fine-Scale Considerations: Moments, Couple Stress, Inhomogeneity, and Energetics
- 8 Time Averaging and Systems with Changing Material Content
- 9 Elements of Mixture Theory
- 10 Fluid Flow through Porous Media
- 11 Linkage of Microscopic and Macroscopic Descriptions of Material Behaviour via Cellular Averaging
- 12 Modelling the Behaviour of Specific Materials: Constitutive Relations and Objectivity
- 13 Comments on Non-Local Balance Relations
- 14 Elements of Classical Statistical Mechanics
- 15 Summary and Suggestions for Further Study
- Appendix A Vectors, Vector Spaces, and Linear Algebra
- Appendix B Calculus in Euclidean Point Space ℰ
- References
- Index
Summary
This work is intended to supplement and complement standard texts on continuum mechanics by drawing attention to physical assumptions implicit in continuum modelling. Particular attention is paid to linking continuum concepts, fields, and relations with underlying molecular behaviour via local averaging in both space and time. The aim is to clarify physical interpretations of concepts and fields and in so doing provide a sound basis for future studies. The contents should be of interest to engineers, mathematicians, and physicists who study macroscopic material behaviour.
The contents are the result of a long-standing study of formal and axiomatic presentations of continuum mechanics. Some of the issues were first addressed in courses delivered under the auspices of CISM (Udine, 1986, 1987), University of Cairo (1994, 1996), and AMAS (Warsaw, 2002; Bydgoszcz, 2003), and other topics treated in published papers. Here the opportunity has been taken to elaborate upon and extend earlier works and to present a unified, more readily accessible treatment of the subject matter.
Given the differing backgrounds of the intended readership, two extensive appendices have been included which develop relevant mathematical concepts and results. In particular, the use of direct (i.e., co-ordinate-free) notation is explained and related to that of Cartesian tensors.
No work exists in isolation: the author is above all indebted to his teachers Mort Gurtin and Walter Noll who introduced him to the mathematical precision and clarity of exposition to be found in modern continuum mechanics.
- Type
- Chapter
- Information
- Physical Foundations of Continuum Mechanics , pp. xiii - xivPublisher: Cambridge University PressPrint publication year: 2012