Discrete Mechanics 1st Edition by Jean-Paul Caltagirone ISBN 978-1848216785 1848216785

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Product details: 

ISBN 10:  1848216785

ISBN 13: 978-1848216785

Author: Jean-Paul Caltagirone 

This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the Helmholtz-Hodge decomposition plays an important role.

Table of contents: 

CHAPTER 1. FRAMEWORK OF DISCRETE MECHANICS

1.1. Frames of reference and uniform motions

1.2. Concept of a Discrete Medium

1.2.1. Vectors and components

1.2.2. Physical meaning of the differential operators

1.2.3. Use of the theorems of differential geometry

1.2.4. Two essential properties

1.2.5. Tensorial values

1.2.6. The scalar and vectorial potentials

1.3. The physical characteristics

1.4. Equilibrium stress state

1.4.1. Two examples of mechanical equilibrium

1.5. Thermodynamic non-equilibrium

1.5.1. Forces and fluxes

1.6. Conservation of mass

CHAPTER 2. MOMENTUM CONSERVATION

2.1. Classification of forces.

2.2. Three fundamental experiments

2.2.1. Equilibrium in a glass of water

2.2.2. Couette flow

2.2.3. Poiseuille flow

2.3. Postulates

2.4. Modeling of the pressure forces

2.5. Modeling of the viscous forces

2.5.1. Modeling of the viscous effects of volume

2.5.2. Modeling of the viscous surface effects

2.5.3. Stress state

2.6. Objectivity

2.7. Discrete motion balance equation

2.7.1. Fundamental law of dynamics

2.7.2. Eulerian step

2.7.3. Mechanical equilibrium

2.8. Formulation in terms of density and temperature

2.9. Similitude parameters

2.9.1. Impact on the surface of a liquid

2.10. Hypercompressible media

CHAPTER 3. CONSERVATION OF HEAT FLUX AND ENERGY

3.1. Introduction

3.2. Conservation of flux

3.3. Conservation of energy

3.3.1. Conservation of total energy

3.3.2. Conservation of kinetic energy

3.3.3. Conservation of the internal energy

3.4. Discrete equations for the flux and the energy

3.5. A simple heat-conduction problem

3.5.1. Case of anisotropic materials

CHAPTER 4. PROPERTIES OF DISCRETE EQUATIONS

4.1. A system of equations and potentials

4.2. Physics represented.

4.2.1. Poiseuille flow and potentials

4.2.2. Celerity and maximum velocity

4.2.3. Remarks about turbulence

4.3. Boundary conditions

4.3.1. Contact surface

4.3.2. Shockwaves

4.3.3. Edge conditions

4.3.4. Slip condition

4.3.5. Capillary effects

4.3.6. Thermal boundary conditions

4.4. Penalization of the potentials

4.5. Continua and discrete mediums

4.5.1. Differences with the Navier-Stokes equation

4.5.2. Dissipation

4.5.3. Case of rigidifying motions

4.5.4. An example of the dissipation of energy

4.6. Hodge-Helmholtz decomposition

4.7. Approximations.

4.7.1. Bernoulli’s law

4.7.2. Irrotational flow

4.7.3. Inviscid fluid

4.7.4. Incompressible flow

4.8. Gravitational waves

4.9. Linear visco-elasticity

4.9.1. Viscous dissipation in a visco-elastic medium

4.9.2. Dissipation of longitudinal waves in a visco-elastic medium

4.9.3. Consistency with Continuum Mechanics

4.9.4. Pure compression

4.9.5. Pure shear stress

4.9.6. Bingham fluid

CHAPTER 5. MULTIPHYSICS

5.1. Extensions to other branches of physics

5.1.1. Coupling between a fluid and a porous medium

5.2. Flow around a cylinder in an infinite medium

5.2.1. Darcian model

5.2.2. Stokes model

5.2.3. Model of an ideal fluid.

5.2.4. Brinkman model

5.3. Fluid statics

5.3.1. Perfect gas in isothermal evolution

5.3.2. Perfect gas in adiabatic evolution

5.4. Injection of a gas into a cavity.

5.4.1. Isothermal injection

5.4.2. Adiabatic injection

5.5. Nonlinear wave propagation

5.5.1. Sod shock tube

5.6. Thermo-acoustics

5.6.1. Heating of a cavity filled with air

5.7. Natural convection in an enclosed cavity

5.8. Multi-component transport

5.9. Modeling of phase change

5.10. Critical opalescence.

5.11. Conclusions regarding the multiphysics approach

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Tags: Jean-Paul Caltagirone, Discrete Mechanics