Synopses & Reviews
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.
Synopsis
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.
Synopsis
This book covers new theoretical and numerical developments in the mechanics of material forces. 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 force, 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.
Table of Contents
Preface
Contributing Authors
Part I. 4d Formalism
1. On establishing balance and conservation laws in elastodynamics (George Herrmann, Reinhold Kienzler)
2. From mathematical physics to engineering science (Gérard A. Maugin)
Part II. Evolving Interfaces
3. The unifying nature of the configurational force balance (Eliot Fried, Morton E. Gurtin)
4. Generalized Stefan models (Alexandre Danescu)
5. Explicit kinetic relation from "first principles" (Lev Truskinovsky, Anna Vainchtein)
Part III. Growth & Biomechanics
6. Surface and bulk growth unified (Antonio DiCarlo)
7. Mechanical and thermodynamical modelling of tissue growth using domain derivation techniques (Jean Francois Ganghoffer)
8. Material forces in the context of biotissue remodelling (Krishna Garikipati, Harish Narayanan, Ellen M. Arruda, Karl Grosh, Sarah Calve)
Part IV. Numerical Aspects
9. Error-controlled adaptive finite element methods in nonlinear elastic fracture mechanics (Marcus Rüter, Erwin Stein)
10. Material force method. Continuum damage & thermo-hyperelasticity (Ralf Denzer, Tina Liebe, Ellen Kuhl, Franz Josef Barth, Paul Steinmann)
11. Discrete material forces in the finite element method (Ralf Mueller, Dietmar Gross)
12. Computational spatial and material settings of continuum mechanics. An arbitrary Lagrangian Eulerian formulation (Ellen Kuhl, Harm Askes, Paul Steinmann)
Part V. Dislocations & Peach-Koehler-Forces
13. Self-driven continuous dislocations and growth (Marcelo Epstein)
14. Role of the non-Riemannian plastic connection in finite elastoplasticity with continuous distribution of dislocations (Sanda Cleja-Tigoiu)
15. Peach-Koehler forces within the theory of nonlocal elasticity (Markus Lazar)
Part VI. Multiphysics & Microstructure
16. On the material energy-momentum tensor in electrostatics and magnetostatics (Carmine Trimarco)
17. Continuum thermodynamic and variational models for continua with microstructure and material inhomogeneity (Bob Svendsen)
18. A crystal structure-based eigentransformation and its work-conjugate material stress (Chien H. Wu)
Part VII. Fracture & Structural Optimization
19. Teaching fracture mechanics within the theory of strength-of-materials (Reinhold Kienzler, George Herrmann)
20. Configurational thermomechanics and crack driving forces (Cristian Dascalu, Vassilios K. Kalpakides)
21. Structural optimization by material forces (Manfred Braun)
22. On structural optimisation and configurational mechanics (Franz-Joseph Barthold)
Part VIII. Path Integrals
23. Configurational forces and the propagation of a circular crack in an elastic body (Vassilios K. Kalpakides, Eleni K. Agiasofitou)
24. Thermoplastic M integral and path domain dependence (Pascal Sansen, Philippe Dufrénoy, Dieter Weichert)
Part IX. Delamination & Discontinuities
25. Peeling tapes (Paolo Podio-Guidugli)
26. Stability and bifurcation with moving discontinuities (Claude Stolz, Rachel-Marie Pradeilles-Duval)
27. On Fracture Modelling Based on Inverse Strong Discontinuities (Ragnar Larsson, Martin Fagerström)
Part X. Interfaces & Phase Transition
28. Maxwell's relation for isotropic bodies (Miroslav