Steinmann Mechanics of Material Forces

1. Auflage 2006
ISBN: 978-0-387-26261-1
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 338 Seiten

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.

Autoren/Hrsg.

Steinmann, Paul

Inhaltsverzeichnis

1;Contents;5
2;Preface;9
3;Contributing Authors;12
4;I 4D FORMALISM;15
4.1;Chapter 1 ON ESTABLISHING BALANCE AND CON-SERVATION LAWS IN ELASTODYNAMICS;16
4.2;Chapter 2 FROM MATHEMATICAL PHYSICS TO ENGINEERING SCIENCE;26
5;II EVOLVING INTERFACES;36
5.1;Chapter 3 THE UNIFYING NATURE OF THE CONFIGURATIONAL FORCE BALANCE;37
5.2;Chapter 4 GENERALIZED STEFAN MODELS;45
5.3;Chapter 5 EXPLICIT KINETIC RELATION FROM " FIRST PRINCIPLES";54
6;III GROWTH & BIOMECHANICS;62
6.1;Chapter 6 SURFACE AND BULK GROWTH UNIFIED;63
6.2;Chapter 7 MECHANICAL AND THERMODYNAMICAL MODELLING OF TISSUE GROWTH USING DOMAIN DERIVATION TECHNIQUES;75
6.3;Chapter 8 MATERIAL FORCES IN THE CONTEXT OF BIOTISSUE REMODELLING;86
7;IV NUMERICAL ASPECTS;94
7.1;Chapter 9 ERROR- CONTROLLED ADAPTIVE FINITE ELEMENT METHODS IN NONLINEAR ELASTIC FRACTURE MECHANICS;95
7.2;Chapter 10 MATERIAL FORCE METHOD. CONTINUUM DAMAGE & THERMO HYPERELASTICITY;103
7.3;Chapter 11 DISCRETE MATERIAL FORCES IN THE FINITE ELEMENT METHOD;113
7.4;Chapter 12 COMPUTATIONAL SPATIAL AND MATERIAL SETTINGS OF CONTINUUM MECHANICS. AN ARBITRARY LAGRAN-GIAN EULERIAN FORMULATION;123
8;V DISLOCATIONS & PEACH- KOEHLER-FORCES;134
8.1;Chapter 13 SELF- DRIVEN CONTINUOUS DISLOCATIONS AND GROWTH;135
8.2;Chapter 14 ROLE OF THE NON- RIEMANNIAN PLAS-TIC CONNECTION IN FINITE ELASTO-PLASTICITY WITH CONTINUOUS DIS-TRIBUTION OF DISLOCATIONS;146
8.3;Chapter 15 PEACH- KOEHLER FORCES WITHIN THE THEORY OF NONLOCAL ELASTICITY;154
9;VI MULTIPHYSICS & MICRO STRUCTURE;164
9.1;Chapter 16 ON THE MATERIAL ENERGY-MOMENTUM TENSOR IN ELECTROSTATICS AND MAGNETOSTATICS;165
9.2;Chapter 17 CONTINUUM THERMODYNAMIC AND VARIATIONAL MODELS FOR CONTINUA WITH MICROSTRUCTURE AND MATERIAL INHOMOGENEITY;176
9.3;Chapter 18 A CRYSTAL STRUCTURE-BASED EIGENTRANSFORMATION AND ITS WORK-CONJUGATE MATERIAL STRESS;184
10;VII FRACTURE & STRUCTURAL OPTIMIZA-TION;193
10.1;Chapter 19 TEACHING FRACTURE MECHANICS WITHIN THE THEORY OF STRENGTH- OF- MATERIALS;194
10.2;Chapter 20 CONFIGURATIONAL THERMOMECH-ANICS AND CRACK DRIVING FORCES;204
10.3;Chapter 21 STRUCTURAL OPTIMIZATION BY MATERIAL FORCES;212
10.4;Chapter 22 ON STRUCTURAL OPTIMISATION AND CONFIGURATIONAL MECHANICS;220
11;VIII PATH INTEGRALS;230
11.1;Chapter 23 CONFIGURATIONAL FORCES AND THE PROPAGATION OF A CIRCULAR CRACK IN AN ELASTIC BODY;231
11.2;Chapter 24 THERMOPLASTIC M INTEGRAL AND PATH DOMAIN DEPENDENCE;240
12;IX DELAMINATION & DISCONTINUITIES;249
12.1;Chapter 25 PEELING TAPES;250
12.2;Chapter 26 STABILITY AND BIFURCATION WITH MOVING DISCONTINUITIES;258
12.3;Chapter 27 ON FRACTURE MODELLING BASED ON INVERSE STRONG DISCONTINUITIES;266
13;INTERFACES & PHASE TRANSITION;275
13.1;Chapter 28 MAXWELL'S RELATION FOR ISOTROPIC BODIES;276
13.2;Chapter 29 DRIVING FORCE IN SIMULATION OF PHASE TRANSITION FRONT PROPAGATION;284
13.3;Chapter 30 MODELING OF THE THERMAL TREAT-MENT OF STEEL WITH PHASE CHANGES;293
14;PLASTICITY & DAMAGE;303
14.1;Chapter 31 CONFIGURATIONAL STRESS TENSOR IN ANISOTROPIC DUCTILE CONTINUUM DAMAGE MECHANICS;304
14.2;Chapter 32 SOME CLASS OF SG CONTINUUM MOD ELS TO CONNECT VARIOUS LENGTH SCALES IN PLASTIC DEFORMATION;312