Mechanics of Material Forces (Advances in Mechanics and Mathematics Book 11)

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. 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 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.

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.

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. This book covers theoretical and numerical developments in the mechanics of material forces.