Читать книгу The Physics of the Deformation of Densely Packed Granular Materials - M A C Koenders - Страница 5

In the early 1980s, the idea first took hold that the mechanical response of a dense granular medium can be understood from a basis of the inter-particle contact properties. The initial efforts, a mean-field theory, had very poor results and papers on ‘micro-mechanics’ were usually relegated to the last section of conference proceedings. Gradually, the insight came about that a granular medium cannot be captured in a mean-field theory and that some form of non-homogeneity in the fabric properties has to be accounted for. The beginnings of this concept were implemented using the available continuum theories on heterogeneity and a few papers came out in the early 90s showing that in certain special cases the mechanical response was captured, but — irritatingly — not all cases. Highly anisotropic packed beds, for example, could not be accounted for and the failure of a granular medium at high stress ratio remained a mystery.

While progress since then has been slow, it is now clear that a proper theory of granular deformation must include a method that deals with heterogeneity that is particularly applicable to a system of particles. This turns out to be the theory of ‘connected media’, which captures the physics of contacting particulates in an appropriate manner. It has also been extended to anisotropic cases. A rigorous approach to Coulomb friction as an inter-particle interaction is required as well. Together these developments can now be implemented with great success.

To preserve analytical insight it is advantageous to use simplified models with round particles and on occasion do a two-dimensional calculation, rather than a three-dimensional one. This does not matter for the understanding of the physics that is at play. The theories have also been applied successfully to other fields where the inter-particle interaction has a more chemical character. Filter cake formation (relevant to chemical engineering) is an example. Due to the large number of natural occurrences and applications of dense granular matter there is relevance in a variety of disciplines.

This book presents a detailed exposition of all the concepts and mathematical techniques that are necessary to understand the current state of the subject. The student from a non-mathematical background may initially have to put in a certain amount of work to grasp the intricacies of the line of argument. This is a very algebraic subject; there is not much one can do about that. However, a mathematical appendix and an introductory chapter on continuum mechanics and Cartesian tensor calculus are provided to make the journey easier.

Curt Koenders Canterbury, 2019