Mechanics of Material Forces (eBook)

Paul Steinmann, Gérard A. Maugin (Herausgeber)

eBook Download: PDF

2006 | 2005
XVI, 338 Seiten
Springer US (Verlag)
978-0-387-26261-1 (ISBN)

Infos

The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de­ ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math­ ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con­ tinuum mechanics. It is more or less clear that seemingly different phe­ nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten­ sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com­ mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the 'driving force' causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.

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The notion dealt with in this volume of proceedings is often traced back to the late 19th-century writings of a rather obscure scientist, C. V. Burton. A probable reason for this is that the painstaking de- ciphering of this author's paper in the Philosophical Magazine (Vol. 33, pp. 191-204, 1891) seems to reveal a notion that was introduced in math- ematical form much later, that of local structural rearrangement. This notion obviously takes place on the material manifold of modern con- tinuum mechanics. It is more or less clear that seemingly different phe- nomena - phase transition, local destruction of matter in the form of the loss of local ordering (such as in the appearance of structural defects or of the loss of cohesion by the appearance of damage or the exten- sion of cracks), plasticity, material growth in the bulk or at the surface by accretion, wear, and the production of debris - should enter a com- mon framework where, by pure logic, the material manifold has to play a prominent role. Finding the mathematical formulation for this was one of the great achievements of J. D. Eshelby. He was led to consider the apparent but true motion or displacement of embedded material inhomogeneities, and thus he began to investigate the "e;driving force"e; causing this motion or displacement, something any good mechanician would naturally introduce through the duahty inherent in mechanics since J. L. d'Alembert.

Inhalt

Contents 5
Preface 9
Contributing Authors 12
I 4D FORMALISM 15
Chapter 1 ON ESTABLISHING BALANCE AND CON-SERVATION LAWS IN ELASTODYNAMICS 16
Chapter 2 FROM MATHEMATICAL PHYSICS TO ENGINEERING SCIENCE 26
II EVOLVING INTERFACES 36
Chapter 3 THE UNIFYING NATURE OF THE CONFIGURATIONAL FORCE BALANCE 37
Chapter 4 GENERALIZED STEFAN MODELS 45
Chapter 5 EXPLICIT KINETIC RELATION FROM " FIRST PRINCIPLES" 54
III GROWTH & BIOMECHANICS
Chapter 6 SURFACE AND BULK GROWTH UNIFIED 63
Chapter 7 MECHANICAL AND THERMODYNAMICAL MODELLING OF TISSUE GROWTH USING DOMAIN DERIVATION TECHNIQUES 75
Chapter 8 MATERIAL FORCES IN THE CONTEXT OF BIOTISSUE REMODELLING 86
IV NUMERICAL ASPECTS 94
Chapter 9 ERROR- CONTROLLED ADAPTIVE FINITE ELEMENT METHODS IN NONLINEAR ELASTIC FRACTURE MECHANICS 95
Chapter 10 MATERIAL FORCE METHOD. CONTINUUM DAMAGE & THERMO HYPERELASTICITY
Chapter 11 DISCRETE MATERIAL FORCES IN THE FINITE ELEMENT METHOD 113
Chapter 12 COMPUTATIONAL SPATIAL AND MATERIAL SETTINGS OF CONTINUUM MECHANICS. AN ARBITRARY LAGRAN-GIAN EULERIAN FORMULATION 123
V DISLOCATIONS & PEACH- KOEHLER-FORCES
Chapter 13 SELF- DRIVEN CONTINUOUS DISLOCATIONS AND GROWTH 135
Chapter 14 ROLE OF THE NON- RIEMANNIAN PLAS-TIC CONNECTION IN FINITE ELASTO-PLASTICITY WITH CONTINUOUS DIS-TRIBUTION OF DISLOCATIONS 146
Chapter 15 PEACH- KOEHLER FORCES WITHIN THE THEORY OF NONLOCAL ELASTICITY 154
VI MULTIPHYSICS & MICRO STRUCTURE
Chapter 16 ON THE MATERIAL ENERGY-MOMENTUM TENSOR IN ELECTROSTATICS AND MAGNETOSTATICS 165
Chapter 17 CONTINUUM THERMODYNAMIC AND VARIATIONAL MODELS FOR CONTINUA WITH MICROSTRUCTURE AND MATERIAL INHOMOGENEITY 176
Chapter 18 A CRYSTAL STRUCTURE-BASED EIGENTRANSFORMATION AND ITS WORK-CONJUGATE MATERIAL STRESS 184
VII FRACTURE & STRUCTURAL OPTIMIZA-TION
Chapter 19 TEACHING FRACTURE MECHANICS WITHIN THE THEORY OF STRENGTH- OF- MATERIALS 194
Chapter 20 CONFIGURATIONAL THERMOMECH-ANICS AND CRACK DRIVING FORCES 204
Chapter 21 STRUCTURAL OPTIMIZATION BY MATERIAL FORCES 212
Chapter 22 ON STRUCTURAL OPTIMISATION AND CONFIGURATIONAL MECHANICS 220
VIII PATH INTEGRALS 230
Chapter 23 CONFIGURATIONAL FORCES AND THE PROPAGATION OF A CIRCULAR CRACK IN AN ELASTIC BODY 231
Chapter 24 THERMOPLASTIC M INTEGRAL AND PATH DOMAIN DEPENDENCE 240
IX DELAMINATION & DISCONTINUITIES
Chapter 25 PEELING TAPES 250
Chapter 26 STABILITY AND BIFURCATION WITH MOVING DISCONTINUITIES 258
Chapter 27 ON FRACTURE MODELLING BASED ON INVERSE STRONG DISCONTINUITIES 266
INTERFACES & PHASE TRANSITION
Chapter 28 MAXWELL'S RELATION FOR ISOTROPIC BODIES 276
Chapter 29 DRIVING FORCE IN SIMULATION OF PHASE TRANSITION FRONT PROPAGATION 284
Chapter 30 MODELING OF THE THERMAL TREAT-MENT OF STEEL WITH PHASE CHANGES 293
PLASTICITY & DAMAGE
Chapter 31 CONFIGURATIONAL STRESS TENSOR IN ANISOTROPIC DUCTILE CONTINUUM DAMAGE MECHANICS 304
Chapter 32 SOME CLASS OF SG CONTINUUM MOD ELS TO CONNECT VARIOUS LENGTH SCALES IN PLASTIC DEFORMATION 312

Produkt-Details

• Erscheint lt. Verlag: 20.1.2006
• Reihe/Serie: Advances in Mechanics and Mathematics
• Reihe/Serie: Advances in Mechanics and Mathematics
• Zusatzinfo: XVI, 338 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Continuum Mechanics • linear optimization • materials mechanics • Mathematical Physics • mechanical engineering • Mechanics • Modeling • Modelling • Numerical Methods • Optimization • Simulation • solid mechanics • stability • Transformation
• ISBN-10: 0-387-26261-X / 038726261X
• ISBN-13: 978-0-387-26261-1 / 9780387262611