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Duality, symmetry and symmetry lost in solid mechanics

Duality, symmetry and symmetry lost in solid mechanics

Selected works of H.D. BUI

Auteur(s) : Alain Ehrlacher, Xanthippi Markenscoff

ISBN : 978-2-85978-458-4, 2011

404 pages, 17 x 24 cm, broché, texte langue anglaise

Prix Internet* 80,00 €
* Ne concerne que le paiement en ligne par CB.

This book collects many of H.D. Bui's works mostly in French, and mostly unknown to the English scientific community, in the fields of Duality, Symmetry in Conservation Laws, Complementarity and Symmetry Lost. The concepts are seldom fully recognized in the literature and, in this sense, this book is unique. To quote Bui: "Duality is synonym of parallelism, or complementary things, sometimes opposite things, tied together in an integral whole". The concept of Duality is closely linked to the concept of "virtual power" in the Mechanics of continuous media; it originates from the concept of spaces and dual spaces of functions in mathematics culminating in the Theory of Distributions by Laurent Schwarz. H.D. Bui exploited the richness of duality to solve elegantly some important and deep inverse engineering problems presented in this book.

 

It contains a total of 31 papers, including one on the application of complementarity to explain the construction of Kheops's pyramid. For his fundamental contributions to Mechanics H.D. Bui was elected to the French Academy of Sciences in 1995 and the European Academy of Sciences in 2001. The presentation of the printed edition of this book coincides with an Internation Colloquium in his honor in Paris on July 4-5, 2011, with the participation of a large number of distinguished scientists representing the US Academy of Sciences, the US Academy of Engineering, the Royal Society of London, ax well as the Russian Academy of Sciences and the French Academy of Sciences.

Sommaire

Foreword

Preface

Biography of H.D. Bui

 

 

Part I : Duality, symmetry and conservation laws

 

- Duality between path independent integrals in fracture mechanics

- Uncoupling the mixed mode of fracture by two new path mechanicals quantities

- A conservation law in linear thermoelasticity

- Extraction of dynamics stress intensity factors from global mechanical quantities

- Symmetry, duality and conjugate variables in boundary integral equations

- Conservation laws in linea thermoelasticity

- On Prandtl's lifting equation arising in wear elasticity

- An integral equations method for solving the problem of a plane crack of arbitrary shape

- Duality and symmetry lost in solid mechanics

- Reciprocity principle and crack identification

- Dissipation of energy in plastic deformation

- On hardening and softening of elasto-plastic materials

 

 

Part II : Duality, symmetry and inverse problems

 

- Inverse acoustic scattering of a planar crack: Closed form solution for a bounded solid

- On some inverse problems in elasticity

- Spatial localization of the error on constitutive law for identification of defects in elastic bodies

- Crack detection by a geometrical approach

- Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap

- On a nonlinear inverse problem in viscoelasticity

- A partial solution to a nonlinear inverse problem

- On complementary theories of the Cheops pyramid construction

 

 

Part III : Application fo fracture mechanics, plasticity and damage

 

- On the hardening of metals

- A generalization of the Griffith theory of fracture

- The weak "thorn" singularity of a bi-material junction in thermo-elasto-plasticity

- Stress ingularities at the angular crack tip

- Infinitesimal deviation of a crack in an arbitrary direction

- Propagation of damage in elastic and plastic solids

- Singular stress fields at the crack tip: A review paper

- Analytical models of fluid flow through a longitudinal crack in a cylindrical shell

- Dynamic crack propagation in thermoelasticity

- The sliding interface crack with friction between elastic and rigid bodies

- Interaction between the Griffith crack and a fluid: Theory of Rehbinder's effect

- Hydrostatic interaction of a wetting fluid and a circular crack in an elastic material

- An integral equationapproach for a planar edge crack emerging at the free surface

- Saint-Venant's principle is a theorem

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Duality, symmetry and symmetry lost in solid mechanics - Selected works of H.D. Bui - Alain Ehrlacher, Xanthippi Markenscoff

Biography of H.D. Bui - Duality, symmetry and conservations laws - Fracture mechanics - Linear thermoelasticity - Hamiltonian structure - Solid mechanics - Reciprocity principle - Crack identification - Plastic deformation - elasto-plastic materials - Inverse acoustic - Spatial localization - 2D elastodynamics - Viscoelasticity - Griffith theory of fracture - Hydrostatic interaction - Elastic material

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