Ebook: Modeling and Mechanics of Granular and Porous Materials

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.

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The modeling of granular and porous materials in science and engineering affects a variety of problems that arise from the need to describe successfully the behavior of materials that exist naturally in our surroundings. Indeed, the modeling process is a critical tool in analyzing and describing the micromechanics and behavior of granular and porous material experimentation.

This work covers all major topics in modeling soil behavior, including transport phenomena: namely, mechanics of porous and granular media, flow and transport phenomena in particulate materials, and numerical simulation methods.

Key features:

* Scientists from different backgrounds, namely engineers and mathematicians who are interested in soil behavior, as well as experts in particulate material modeling, focus on the most important techniques and models currently in use

* Contributions are devoted to both the mathematical and engineering aspects of the subject and bring the reader to the frontiers of research

* Numerical models given for finite elastoplastic deformations

Modeling and Mechanics of Granular and Porous Materials is fairly unique in the literature. It may serve as both an excellent reference text or in seminars, appealing to graduate students, researchers and scientists in applied mathematics, continuum mechanics, finite element methods, solid mechanics, and hydraulics engineering. A good foundation in continuum mechanics is a prerequisite.

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The modeling of granular and porous materials in science and engineering affects a variety of problems that arise from the need to describe successfully the behavior of materials that exist naturally in our surroundings. Indeed, the modeling process is a critical tool in analyzing and describing the micromechanics and behavior of granular and porous material experimentation.

This work covers all major topics in modeling soil behavior, including transport phenomena: namely, mechanics of porous and granular media, flow and transport phenomena in particulate materials, and numerical simulation methods.

Key features:

* Scientists from different backgrounds, namely engineers and mathematicians who are interested in soil behavior, as well as experts in particulate material modeling, focus on the most important techniques and models currently in use

* Contributions are devoted to both the mathematical and engineering aspects of the subject and bring the reader to the frontiers of research

* Numerical models given for finite elastoplastic deformations

Modeling and Mechanics of Granular and Porous Materials is fairly unique in the literature. It may serve as both an excellent reference text or in seminars, appealing to graduate students, researchers and scientists in applied mathematics, continuum mechanics, finite element methods, solid mechanics, and hydraulics engineering. A good foundation in continuum mechanics is a prerequisite.

Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Constitutive Equations and Instabilities of Granular Materials....Pages 3-43
Micromechanical Modeling of Granular Materials....Pages 45-61
Thermodynamic Modeling of Granular Continua Exhibiting Quasi-Static Frictional Behaviour with Abrasion....Pages 63-83
Modeling of Soil Behaviour: from Micro-Mechanical Analysis to Macroscopic Description....Pages 85-127
Dynamic Thermo-Poro-Mechanical Stability Analysis of Simple Shear on Frictional Materials....Pages 129-155
Front Matter....Pages 157-157
Mathematical Models for Soil Consolidation Problems: a State of the Art Report....Pages 159-180
Flow of Water in Rigid and Non-Rigid, Saturated and Unsaturated Soils....Pages 181-210
Mass Exchange, Diffusion and Large Deformations of Poroelastic Materials....Pages 211-242
Front Matter....Pages 243-243
Continuum and Numerical Simulation of Porous Materials in Science and Technology....Pages 245-292
A Mathematical and Numerical Model for Finite Elastoplastic Deformations in Fluid Saturated Porous Media....Pages 293-340
Numerical Modeling of Initiation and Propagation Phases of Landslides....Pages 341-369

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The modeling of granular and porous materials in science and engineering affects a variety of problems that arise from the need to describe successfully the behavior of materials that exist naturally in our surroundings. Indeed, the modeling process is a critical tool in analyzing and describing the micromechanics and behavior of granular and porous material experimentation.

This work covers all major topics in modeling soil behavior, including transport phenomena: namely, mechanics of porous and granular media, flow and transport phenomena in particulate materials, and numerical simulation methods.

Key features:

* Scientists from different backgrounds, namely engineers and mathematicians who are interested in soil behavior, as well as experts in particulate material modeling, focus on the most important techniques and models currently in use

* Contributions are devoted to both the mathematical and engineering aspects of the subject and bring the reader to the frontiers of research

* Numerical models given for finite elastoplastic deformations

Modeling and Mechanics of Granular and Porous Materials is fairly unique in the literature. It may serve as both an excellent reference text or in seminars, appealing to graduate students, researchers and scientists in applied mathematics, continuum mechanics, finite element methods, solid mechanics, and hydraulics engineering. A good foundation in continuum mechanics is a prerequisite.

Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Constitutive Equations and Instabilities of Granular Materials....Pages 3-43
Micromechanical Modeling of Granular Materials....Pages 45-61
Thermodynamic Modeling of Granular Continua Exhibiting Quasi-Static Frictional Behaviour with Abrasion....Pages 63-83
Modeling of Soil Behaviour: from Micro-Mechanical Analysis to Macroscopic Description....Pages 85-127
Dynamic Thermo-Poro-Mechanical Stability Analysis of Simple Shear on Frictional Materials....Pages 129-155
Front Matter....Pages 157-157
Mathematical Models for Soil Consolidation Problems: a State of the Art Report....Pages 159-180
Flow of Water in Rigid and Non-Rigid, Saturated and Unsaturated Soils....Pages 181-210
Mass Exchange, Diffusion and Large Deformations of Poroelastic Materials....Pages 211-242
Front Matter....Pages 243-243
Continuum and Numerical Simulation of Porous Materials in Science and Technology....Pages 245-292
A Mathematical and Numerical Model for Finite Elastoplastic Deformations in Fluid Saturated Porous Media....Pages 293-340
Numerical Modeling of Initiation and Propagation Phases of Landslides....Pages 341-369
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