Mechanics of Material Forces (Advances in Mechanics and Mathematics)

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. 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 (Grard 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 Rter, 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 Dufrnoy, 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 Fagerstrm) Part X. Interfaces & Phase Transition 28. Maxwell’s relation for isotropic bodies (Miroslav silhav) 29. Driving force in simulation of phase transition front propagation (Arkadi Berezovski, Grard A. Maugin) 30. Modeling of the thermal treatment of steel with phase changes (Serguei Dachkovski, Michael Bhm) Part XI. Plasticity & Damage 31. Configurational stress tensor in anisotropic ductile continuum damage mechanics (Michael Brnig) 32. Some class of SG Continuum models to connect various length scales in plastic deformation (Lalaonirina Rakotomanana) 33. Weakly nonlocal theories of damage and plasticity based on balance of dissipative material forces (Helmut Stumpf, Jerzy Makowski, Jaroslaw Gorski, Klaus Hackl)