Mechanics of Material Forces

George Herrmann, Reinhold Kienzler (auth.), Paul Steinmann, Gérard A. Maugin (eds.)0387262601, 9780387262604, 9780387262611, 038726261X

In this single volume the reader will find all recent developments in one of the most promising and rapidly expanding branches of continuum mechanics, the mechanics of material forces. The book covers both theoretical and numerical developments. Conceptually speaking, common continuum mechanics in the sense of Newton—which gives rise to the notion of spatial (mechanical) forces—considers the response to variations of spatial placements of “physical particles” with respect to the ambient space, whereas continuum mechanics in the sense of Eshelby—which gives rise to the notion of material (configurational) forces—is concerned with the response to variations of material placements of “physical particles” with respect to the ambient material. Well-known examples of material forces are driving forces on defects like the Peach-Koehler forece, the J-Integral in fracture mechanics, and energy release. The consideration of material forces goes back to the works of Eshelby, who investigated forces on defects; therefore this area of continuum mechanics is sometimes denoted Eshelbian mechanics.

Audience

This book is suitable for civil and mechanical engineers, physicists and applied mathematicians.

Table of contents :
On Establishing Balance and Conservation Laws in Elastodynamics….Pages 1-11
From Mathematical Physics to Engineering Science….Pages 13-22
The Unifying Nature of the Configurational Force Balance….Pages 25-32
Generalized Stefan Models….Pages 33-41
Explicit Kinetic Relation from “First Principles”….Pages 43-50
Surface and Bulk Growth Unified….Pages 53-64
Mechanical and Thermodynamical Modelling of Tissue Growth Using Domain Derivation Techniques….Pages 65-75
Material Forces in the Context of Biotissue Remodelling….Pages 77-84
Error-Controlled Adaptive Finite Element Methods in Nonlinear Elastic Fracture Mechanics….Pages 87-94
Material Force Method. Continuum Damage & Thermo-Hyperelasticity….Pages 95-104
Discrete Material Forces in the Finite Element Method….Pages 105-114
Computational Spatial and Material Settings of Continuum Mechanics. An Arbitrary Lagrangian Eulerian Formulation….Pages 115-125
Self-Driven continuous Dislocations and Growth….Pages 129-139
Role of the Non-Riemannian Plastic Connection in Finite Elasto-Plasticity with Continuous Distribution of Dislocations….Pages 141-148
Peach-Koehler Forces within the Theory of Nonlocal Elasticity….Pages 149-158
On the Material Energy-Momentum Tensor in Electrostatics and Magnetostatics….Pages 161-171
Continuum Thermodynamic and Variational Models for Continua with Microstructure and Material Inhomogeneity….Pages 173-180
A Crystal Structure-Based Eigentransformation and its Work-Conjugate Material Stress….Pages 181-189
Teaching Fracture Mechanics Within the Theory of Strength-of-Materials….Pages 193-202
Configurational Thermomech-Anics and Crack Driving Forces….Pages 203-210
Structural Optimization by Material Forces….Pages 211-218
On Structural Optimisation and Configurational Mechanics….Pages 219-228
Configurational Forces and the Propagation of a Circular Crack in an Elastic Body….Pages 231-239
Thermoplastic M Integral and Path Domain Dependence….Pages 241-249
Peeling Tapes….Pages 253-260
Stability and Bifurcation with Moving Discontinuities….Pages 261-268
On Fracture Modelling Based on Inverse Strong Discontinuities….Pages 269-277
Maxwell’s Relation for Isotropic Bodies….Pages 281-288
Driving Force in Simulation of Phase Transition Front Propagation….Pages 289-297
Modeling of the Thermal Treatment of Steel With Phase Changes….Pages 299-308
Configurational Stress Tensor in Anisotropic Ductile Continuum Damage Mechanics….Pages 309-318
Some Class of SG Continuum Models to Connect Various Length Scales in Plastic Deformation….Pages 319-326
Weakly Nonlocal Theories of Damage and Plasticity Based on Balance of Dissipative Material Forces….Pages 327-337