Ebook: Non-Smooth Thermomechanics

Based on practical problems in mechanical engineering, the author develops in this book the fundamental concepts of non-smooth thermomechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints. From this point, powerful methods for the applied mathematician and the mechanical engineer are derived, and applied to numerous cases including collisions of deformable and non-deformable solids, shape memory alloys, damage of materials, soil freezing, supercooling and solid--liquid phase changes, to name but a few. This book will be of great value to both the researcher and practitioner, but it can also be used as an advanced text for students in civil and mechanical engineering.

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Based on practical problems in mechanical engineering, the author develops in this book the fundamental concepts of non-smooth thermomechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints. From this point, powerful methods for the applied mathematician and the mechanical engineer are derived, and applied to numerous cases including collisions of deformable and non-deformable solids, shape memory alloys, damage of materials, soil freezing, supercooling and solid--liquid phase changes, to name but a few. This book will be of great value to both the researcher and practitioner, but it can also be used as an advanced text for students in civil and mechanical engineering.

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Based on practical problems in mechanical engineering, the author develops in this book the fundamental concepts of non-smooth thermomechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints. From this point, powerful methods for the applied mathematician and the mechanical engineer are derived, and applied to numerous cases including collisions of deformable and non-deformable solids, shape memory alloys, damage of materials, soil freezing, supercooling and solid--liquid phase changes, to name but a few. This book will be of great value to both the researcher and practitioner, but it can also be used as an advanced text for students in civil and mechanical engineering.
Content:
Front Matter....Pages I-XVI
The Description of a Material....Pages 1-2
The Principle of Virtual Power....Pages 3-5
The Constitutive Laws. Case of No Constraint on the State Quantities or Their Velocities....Pages 7-13
The Constitutive Laws. Case with Constraints on the State Quantities....Pages 15-32
The Constitutive Laws on a Discontinuity Surface....Pages 33-58
Deformable Solids with Interactions at a Distance....Pages 59-91
Deformable Solids Without Interaction at a Distance....Pages 93-99
Collision of Rigid Bodies. Multiple Collisions....Pages 101-183
Evolution of Two Deformable Solids with Collisions....Pages 185-218
Material with Volume Interactions at a Distance. Fibre Reinforced Material....Pages 219-247
Solid—Liquid Phase Change. Supercooling. Soil Freezing....Pages 249-311
Damage. Gradient of Damage....Pages 313-357
Shape Memory Alloys....Pages 359-400
Unilateral Contact. Contact with Adhesion....Pages 401-454
Back Matter....Pages 455-480

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Based on practical problems in mechanical engineering, the author develops in this book the fundamental concepts of non-smooth thermomechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints. From this point, powerful methods for the applied mathematician and the mechanical engineer are derived, and applied to numerous cases including collisions of deformable and non-deformable solids, shape memory alloys, damage of materials, soil freezing, supercooling and solid--liquid phase changes, to name but a few. This book will be of great value to both the researcher and practitioner, but it can also be used as an advanced text for students in civil and mechanical engineering.
Content:
Front Matter....Pages I-XVI
The Description of a Material....Pages 1-2
The Principle of Virtual Power....Pages 3-5
The Constitutive Laws. Case of No Constraint on the State Quantities or Their Velocities....Pages 7-13
The Constitutive Laws. Case with Constraints on the State Quantities....Pages 15-32
The Constitutive Laws on a Discontinuity Surface....Pages 33-58
Deformable Solids with Interactions at a Distance....Pages 59-91
Deformable Solids Without Interaction at a Distance....Pages 93-99
Collision of Rigid Bodies. Multiple Collisions....Pages 101-183
Evolution of Two Deformable Solids with Collisions....Pages 185-218
Material with Volume Interactions at a Distance. Fibre Reinforced Material....Pages 219-247
Solid—Liquid Phase Change. Supercooling. Soil Freezing....Pages 249-311
Damage. Gradient of Damage....Pages 313-357
Shape Memory Alloys....Pages 359-400
Unilateral Contact. Contact with Adhesion....Pages 401-454
Back Matter....Pages 455-480
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