On rational treatments of the general laws of balance and jump, with emphasis on configurational formulations

Acta Mechanica

Volumn 194, Issue 1-4, 2007, Pages 11-32

  Irschik, H ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

FORCE MEASUREMENT; LINEAR SYSTEMS; MATHEMATICAL MODELS; MOMENTUM; NUMERICAL METHODS; VECTORS;

DIFFERENTIAL BALANCE LAW; LINEAR MOMENTUM;

INTEGRAL EQUATIONS;

EID: 35648972114     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-007-0485-1     Document Type: Article

References (38)

1. In: Wittgenstein. Ausgewählt und vorgestellt von T. H. Macho. München: Deutscher Taschenbuch Verlag 2001
2. Truesdell C. A. and Toupin R. (1960). The classical field theories. In: Flügge, S. (eds) Handbuch der Physik, Band III/1 Prinzipien der Klassischen Mechanik und Feldtheorie, pp 226-793. Springer, Berlin
3. Reynolds, O.: The sub-mechanics of the universe. Cambridge University Press (Distributed for the Royal Society in London) 1903
4. Irschik H. (2005). Ludwig Wittgenstein und die Mechanik. In: Maaß, J., Langer, U. and Larcher, G. (eds) Kepler Symposium Philosophie und Geschichte der Mathematik, pp 147-163. Universitätsverlag Rudolf Trauner, Linz
5. Liu I.-S. (2002). Continuum mechanics. Springer, Berlin
6. Ziegler F. (1998). Mechanics of solids and fluids, 2nd English ed. corrected 2nd printing. Springer, New York
7. Müller, P.: Two approximations for ∫ H(x) H′(x) dx. Personal communication, Johannes Kepler University of Linz 2006
8. Hofmann A., Marx B. and Vogt W. (2006). Mathematik für Ingenieure, vol. 2. Pearson, München
9. Schwartz L. (1954). Sur l'impossibilite de la multiplication des distributions. C.R. Acad. Sci., Paris 239: 847-848
10. Irschik H. (2003). On the necessity of surface growth terms for the consistency of jump relations at a singular surface. Acta Mech. 162: 195-211
11. Irschik H. (2004). A treatise on the equations of balance and on the jump relations in continuum mechanics. In: Irschik, H. and Schlacher, K. (eds) Advanced dynamics and control of structures and machines, CISM Courses and Lectures, vol. 444, pp 9-20. Springer, Wien New York
12. Eshelby J. D. (1951). Force on an elastic singularity. Phil. Trans. Roy. Soc. Lond. A 244: 87-112
13. Maugin G. A. (1993). Material inhomogenieities in elasticity. Chapman, London
14. Maugin G. A. (1995). Material forces: Concepts and applications. Appl Mech. Rev. 48: 213-245
15. Kientzler R. and Herrmann G. (2000). Mechanics in material space. Springer, Berlin
16. Gurtin M. E. (2000). Configurational forces as basic concepts in continuum physics. Springer, New York
17. Kienzler, R., Maugin, G. A. (eds.): Configurational mechanics of materials, CISM Courses and Lectures, vol. 427. Wien New York: Springer 2001
18. Kienzler R. and Herrmann G. (1986). An elementary theory of defective beams. Acta Mech. 62: 37-46
19. Kienzler R. and Herrmann G. (1997). On the properties of the Eshelby tensor. Acta Mech. 125: 73-91
20. Honein T. and Herrmann G. (1997). Conservation laws in nonhomogeneous plane elastostatics. J. Mech. Phy. Solids 45: 789-805
21. Herrmann G. and Kienzler R. (2001). Conservation laws and their application in configurational mechanics. In: Kienzler, R. and Maugin, G. A. (eds) Configurational mechanics of materials, CISM Courses and Lectures, vol. 427, pp 1-54. Springer, Wien New York
22. Kienzler R. and Herrmann G. (2001). Configurational mechanics applied to strength-of-materials. In: Kienzler, R. and Maugin, G.A. (eds) Configurational mechanics of materials, CISM Courses and Lectures, vol. 427, pp 173-220. Springer, Wien New York
23. Kienzler R. and Herrmann G. (2003). On the four-dimensional formalism in continuum mechanics. Acta Mech. 161: 103-125
24. Kienzler R. and Herrmann G. (2004). On conservation laws in elastodynamics. Int. J. Solids Struct. 41: 3595-3606
25. Kienzler, R., Herrmann, G.: Nonlinear and linearized reciprocity relations in structural configurational mechanics. Acta Mech. DOI 10.1007/s00707-007-0457-5 (2007)
26. Steinmann P. (2002). On spatial and material settings of hyperelastodynamics. Acta Mech. 156: 193-218
27. Kuhl E. and Steinmann P. (2005). A hyperelastodynamic ALE formulation based on referential, spatial and material settings of continuum mechanics. Acta Mech. 174: 201-222
28. Gross D. (2001). Morphological equilibrium and kinetics of two-phase materials. In: Kienzler, R. and Maugin, G. A. (eds) Configurational mechanics of materials, CISM Courses and Lectures, vol. 427, pp 221-272. Springer, Wien New York
29. Gross D., Kolling S., Mueller R. and Schmidt I. (2003). Configurational forces and their application in solid mechanics. Europ. J. Mech. A 22: 669-692
30. Maugin G. A. (2006). On canonical equations of continuum thermomechanics. Mech. Res. Comm. 33: 705-710
31. Abeyaratne R. and Knowles J. K. (1990). On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids 38: 345-360
32. Abeyaratne R. and Knowles J. K. (2006). Evolution of phase transitions: a continuum theory. Cambridge University Press, Cambridge
33. Maugin G. A. (1997). Thermomechanics of inhomogeneous-heterogeneous systems: application to the irreversible progress of two-and three-dimensional defects. ARI (Springer) 49: 41-56
34. Maugin G. A. (1998). On shock waves and phase-transition fronts in continua. ARI (Springer) 50: 141-150
35. Maugin G. A. and Trimarco C. (2001). Elements of field theory in inhomogeneous and defective materials. In: Kienzler, R. and Maugin, G. A. (eds) Configurational mechanics of materials, CISM Courses and Lectures, vol 427, pp 55-128. Springer, Wien New York
36. Berezovski A. and Maugin G. A. (2005). On the velocity of a moving phase boundary in solids. Acta Mech. 179: 187-196
37. Becker E. and Bürger W. (1975). Kontinuumsmechanik. B. G Teubner, Stuttgart
38. Haupt P. (2002). Continuum mechanics and theory of materials. Springer, Berlin