Non-Smooth Thermomechanics

ISBN-13: 9783642085789 / Angielski / Miękka / 2010 / 480 str.

Michel Fremond

Opis

Based on practical problems in mechanical engineering, here the author develops the fundamental concepts of non-smooth mechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints.

Recenzje

"This book offers a fresh point of view and a new unifying approach to several different phenomena involving complex materials in continuum mechanics." (Mathematical Reviews 2003g)

"Providing an introduction to non-smooth thermodynamics and its application to a number of practical problems in mechanics, civil and mechanical engineering, this book appeals to both students (at a graduate level) and researchers." (Zentralblatt MATH, 990/15, 2002)

Spis treści

1. The Description of a Material.- 3. The Constitutive Laws. Case of No Constraint on the State Quantities or Their Velocities.- 5. The Constitutive Laws on a Discontinuity Surface.- 6. Deformable Solids with Interactions at a Distance.- 7. Deformable Solids Without Interaction at a Distance.- 8. Collision of Rigid Bodies. Multiple Collisions.- 9. Evolution of Two Deformable Solids with Collisions.- 10. Material with Volume Interactions at a Distance. Fibre Reinforced Material.- 11. Solid—Liquid Phase Change. Supercooling. Soil Freezing.- 12. Damage. Gradient of Damage.- 13. Shape Memory Alloys.- 14. Unilateral Contact. Contact with Adhesion.- A.1 Convex Functions.- A.1.1 Subgradient of a Convex Function. Subdifferential Set.- A.1.2 Indicator Function of a Set.- A.1.5 Indicator Function of the Segment [0, 1].- A.1.7 Indicator Function of a Triangle.- A.1.9 A Property of the Subdifferential Set.- A.1.10The Dual Function of a Convex Function.- A.2 Material Derivatives.- A.2.1 Material Derivative of a Function.- A.2.2 Material Derivative of a Surface Integral.- A.2.3 Material Derivative of a Double Surface Integral.- A.2.4 Mass Balance on a Surface.- A.2.5 Material Derivatives of Integrals of Mass Densities.- References.

Blurb

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.