Includes bibliographical references.

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 (Gerard 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 Ruter, 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

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.