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Advances in Mechanics and Mathematics #11: Mechanics of Material Forces

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Advances in Mechanics and Mathematics #11: Mechanics of Material Forces Cover

 

Synopses & Reviews

Publisher 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 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:

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

Product Details

ISBN:
9781441938794
Author:
Steinmann, Paul
Publisher:
Springer
Author:
Maugin, Gerard A.
Location:
Boston, MA
Subject:
Physics-Math
Subject:
Applied
Subject:
Continuum mechanics
Subject:
Materials mechanics
Subject:
Mechanical engineering
Subject:
Numerical methods
Subject:
Solid mechanics
Subject:
Mathematical Modeling and Industrial Mathematics
Subject:
Continuum Mechanics and Mechanics of Materials
Subject:
mathematical methods in physics
Subject:
Computational intelligence
Subject:
Mechanics
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Materials
Subject:
Mathematical Physics
Subject:
Engineering
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2005
Series:
Advances in Mechanics and Mathematics
Series Volume:
11
Publication Date:
20101208
Binding:
TRADE PAPER
Language:
English
Pages:
354
Dimensions:
235 x 155 mm 530 gr

Related Subjects

Engineering » Mechanical Engineering » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Physics » Classical Mechanics
Science and Mathematics » Physics » Math

Advances in Mechanics and Mathematics #11: Mechanics of Material Forces New Trade Paper
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Product details 354 pages Springer - English 9781441938794 Reviews:
"Synopsis" by , 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.
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