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Other titles in the Advances in Mechanics and Mathematics series:
Advances in Mechanics and Mathematics #11: Mechanics of Material Forcesby Paul Steinmann
Synopses & ReviewsPublisher Comments: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 Newtonwhich gives rise to the notion of spatial (mechanical) forcesconsiders the response to variations of spatial placements of "physical particles" with respect to the ambient space, whereas continuum mechanics in the sense of Eshelbywhich gives rise to the notion of material (configurational) forcesis concerned with the response to variations of material placements of "physical particles" with respect to the ambient material. Wellknown examples of material forces are driving forces on defects like the PeachKoehler forece, the JIntegral 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: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. Wellknown examples of material forces are driving forces on defects like the PeachKoehler force, the JIntegral 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 ContentsPreface 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. Errorcontrolled adaptive finite element methods in nonlinear elastic fracture mechanics (Marcus Rüter, Erwin Stein) 10. Material force method. Continuum damage & thermohyperelasticity (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 & PeachKoehlerForces 13. Selfdriven continuous dislocations and growth (Marcelo Epstein) 14. Role of the nonRiemannian plastic connection in finite elastoplasticity with continuous distribution of dislocations (Sanda ClejaTigoiu) 15. PeachKoehler forces within the theory of nonlocal elasticity (Markus Lazar) Part VI. Multiphysics & Microstructure 16. On the material energymomentum 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 structurebased eigentransformation and its workconjugate material stress (Chien H. Wu) Part VII. Fracture & Structural Optimization 19. Teaching fracture mechanics within the theory of strengthofmaterials (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 (FranzJoseph 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 PodioGuidugli) 26. Stability and bifurcation with moving discontinuities (Claude Stolz, RachelMarie PradeillesDuval) 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
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