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This special issue collects selected contributions (excluding
general lectures) of a Symposium on "Micro to MACRO Mathematical
Modelling in Soil Mechanics", which took place at the University of
Reggio Calabria, Italy, from May 29th to June 1st, 2018. The
Symposium provided an opportunity to enhance the scientific debate
on the construction of mathematical models for the description of
the physical behaviour of soils, as well as on the suggestions
provided by the micro-mechanical observation of the matter. The
focus was on the comparison between the appropriateness of models
and the need of mathematics to obtain rigorous results, which
involves know-how from applied mathematical physics, geotechnical
engineering and mechanics of solids. The contributions were
selected by the Editors and the other Members of the Scientific
Committee of the Symposium: Gianfranco Capriz (Pisa, Roma), Claudio
di Prisco (Milan), Wolfgang Ehlers (Stuttgart), James T. Jenkins
(Cornell), Stefan Luding (Twente), David Muir Wood (Dundee),
Kenichi Soga (Berkeley).
Soils are complex materials: they have a particulate structure and
fluids can seep through pores, mechanically interacting with the
solid skeleton. Moreover, at a microscopic level, the behaviour of
the solid skeleton is highly unstable. External loadings are in
fact taken by grain chains which are continuously destroyed and
rebuilt. Many issues of modeling, even of the physical details of
the phenomena, remain open, even obscure; de Gennes listed them not
long ago in a critical review. However, despite physical
complexities, soil mechanics has developed on the assumption that a
soil can be seen as a continuum, or better yet as a medium obtained
by the superposition of two and sometimes three con and the other
fluids, which occupy the same portion of tinua, one solid space.
Furthermore, relatively simple and robust constitutive laws were
adopted to describe the stress-strain behaviour and the interaction
between the solid and the fluid continua. The contrast between the
intrinsic nature of soil and the simplistic engi neering approach
is self-evident. When trying to describe more and more
sophisticated phenomena (static liquefaction, strain localisation,
cyclic mo bility, effects of diagenesis and weathering, ..... ),
the nalve description of soil must be abandoned or, at least,
improved. Higher order continua, incrementally non-linear laws,
micromechanical considerations must be taken into account. A new
world was opened, where basic mathematical questions (such as the
choice of the best tools to model phenomena and the proof of the
well-posedness of the consequent problems) could be addressed.
Granular matter displays a variety of peculiarities that
distinguish it from other appearances studied in condensed matter
physics and renders its overall mathematical modelling somewhat
arduous. Prominent directions in the modelling granular flows are
analyzed from various points of view. Foundational issues,
numerical schemes and experimental results are discussed. The
volume furnishes a rather complete overview of the current research
trends in the mechanics of granular matter. Various chapters
introduce the reader to different points of view and related
techniques. New models describing granular bodies as complex bodies
are presented. Results on the analysis of the inelastic Boltzmann
equations are collected in different chapters. Gallavotti-Cohen
symmetry is also discussed.
Soils are complex materials: they have a particulate structure and
fluids can seep through pores, mechanically interacting with the
solid skeleton. Moreover, at a microscopic level, the behaviour of
the solid skeleton is highly unstable. External loadings are in
fact taken by grain chains which are continuously destroyed and
rebuilt. Many issues of modeling, even of the physical details of
the phenomena, remain open, even obscure; de Gennes listed them not
long ago in a critical review. However, despite physical
complexities, soil mechanics has developed on the assumption that a
soil can be seen as a continuum, or better yet as a medium obtained
by the superposition of two and sometimes three con and the other
fluids, which occupy the same portion of tinua, one solid space.
Furthermore, relatively simple and robust constitutive laws were
adopted to describe the stress-strain behaviour and the interaction
between the solid and the fluid continua. The contrast between the
intrinsic nature of soil and the simplistic engi neering approach
is self-evident. When trying to describe more and more
sophisticated phenomena (static liquefaction, strain localisation,
cyclic mo bility, effects of diagenesis and weathering, ..... ),
the nalve description of soil must be abandoned or, at least,
improved. Higher order continua, incrementally non-linear laws,
micromechanical considerations must be taken into account. A new
world was opened, where basic mathematical questions (such as the
choice of the best tools to model phenomena and the proof of the
well-posedness of the consequent problems) could be addressed."
This contributed volume provides an up-to-date overview of the
mechanics of granular materials, ranging from sparse media to
soils. With chapters exploring state-of-the-art theoretical,
experimental, and applied trends in the study of granular matter in
various states, readers will be motivated to learn about the
current challenges and potential avenues of exploration in this
active area of research. Including a variety of perspectives, this
volume will be a valuable reference for audiences in a number of
fields. Specific topics covered include: X-ray tomography
techniques for analyzing sand Evaluation of effective stress in
unsaturated soils Hyper-plasticity Wave propagation in granular
systems Partly saturated porous media Multi-scale approaches to the
dynamics of sparse media Views on Microstructures in Granular
Materials is an ideal resource for PhD students and researchers in
applied mathematics, solid-state physics, civil engineering, and
mechanical engineering.
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