Ebook: Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances

This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

Audience

This book is intended for researchers in mathematics and mechanics.

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This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

 

Audience

This book is intended for researchers in mathematics and mechanics.

---

This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

 

Audience

This book is intended for researchers in mathematics and mechanics.

Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Moreau’s Proximal Mappings and Convexity in Hamilton-Jacobi Theory....Pages 3-12
Three Optimization Problems in Mass Transportation Theory....Pages 13-23
Some Geometrical and Algebraic Properties of Various Types of Convex Hulls....Pages 25-34
A Note on the Legendre-Fenchel Transform of Convex Composite Functions....Pages 35-46
What Is to be a Mean?....Pages 47-57
Front Matter....Pages 59-59
Thermoelastic Contact with Frictional Heating....Pages 61-70
A Condition for Statical Admissibility in Unilateral Structural Analysis....Pages 71-80
Min-Max Duality and Shakedown Theorems in Plasticity....Pages 81-92
Friction and Adhesion....Pages 93-105
The Clausius-Duhem Inequality, an Interesting and Productive Inequality....Pages 107-118
Unilateral Crack Identification....Pages 119-128
Penalty Approximation of Painlev? Problem....Pages 129-143
Discrete Contact Problems with Friction: A Stress-Based Approach....Pages 145-159
Front Matter....Pages 161-161
A Brief History of Drop Formation....Pages 163-172
Semiclassical Approach of the “Tetrad Model” of Turbulence....Pages 173-182
Front Matter....Pages 183-183
The Geometry Of Newton’s Cradle....Pages 185-194
Using Nonsmooth Analysis for Numerical Simulation of Contact Mechanics....Pages 195-207
Numerical Simulation of a Multibody Gas....Pages 209-220
Granular Media and Ballasted Railway Tracks Milieux Granulaires Et Voies Ballast?es....Pages 221-232
Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows....Pages 233-245
Front Matter....Pages 247-247
Morphological Equations and Sweeping Processes....Pages 249-259
Higher Order Moreau’s Sweeping Process....Pages 261-277
An Existence Result in Non-Smooth Dynamics....Pages 279-288
Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction....Pages 289-304
Canonical Duality in Nonsmooth, Constrained Concave Minimization....Pages 305-314
Back Matter....Pages 315-320

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This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

 

Audience

This book is intended for researchers in mathematics and mechanics.

Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Moreau’s Proximal Mappings and Convexity in Hamilton-Jacobi Theory....Pages 3-12
Three Optimization Problems in Mass Transportation Theory....Pages 13-23
Some Geometrical and Algebraic Properties of Various Types of Convex Hulls....Pages 25-34
A Note on the Legendre-Fenchel Transform of Convex Composite Functions....Pages 35-46
What Is to be a Mean?....Pages 47-57
Front Matter....Pages 59-59
Thermoelastic Contact with Frictional Heating....Pages 61-70
A Condition for Statical Admissibility in Unilateral Structural Analysis....Pages 71-80
Min-Max Duality and Shakedown Theorems in Plasticity....Pages 81-92
Friction and Adhesion....Pages 93-105
The Clausius-Duhem Inequality, an Interesting and Productive Inequality....Pages 107-118
Unilateral Crack Identification....Pages 119-128
Penalty Approximation of Painlev? Problem....Pages 129-143
Discrete Contact Problems with Friction: A Stress-Based Approach....Pages 145-159
Front Matter....Pages 161-161
A Brief History of Drop Formation....Pages 163-172
Semiclassical Approach of the “Tetrad Model” of Turbulence....Pages 173-182
Front Matter....Pages 183-183
The Geometry Of Newton’s Cradle....Pages 185-194
Using Nonsmooth Analysis for Numerical Simulation of Contact Mechanics....Pages 195-207
Numerical Simulation of a Multibody Gas....Pages 209-220
Granular Media and Ballasted Railway Tracks Milieux Granulaires Et Voies Ballast?es....Pages 221-232
Scaling Behaviour of Velocity Fluctuations in Slow Granular Flows....Pages 233-245
Front Matter....Pages 247-247
Morphological Equations and Sweeping Processes....Pages 249-259
Higher Order Moreau’s Sweeping Process....Pages 261-277
An Existence Result in Non-Smooth Dynamics....Pages 279-288
Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction....Pages 289-304
Canonical Duality in Nonsmooth, Constrained Concave Minimization....Pages 305-314
Back Matter....Pages 315-320
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