The principle of virtual power: From eliminating metaphysical forces to providing an efficient modelling tool: In memory of Paul Germain (1920-2009)

Continuum Mechanics and Thermodynamics

Volumn 25, Issue 2-4, 2013, Pages 127-146

  Maugin, Gérard A ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Discontinuities; Mechanics of deformable solids; Microstructure; Mixtures; Structures; Thermomechanics; Variational formulation; Virtual power

Indexed keywords

MICROSTRUCTURE; MIXTURES; NUMERICAL METHODS; STRUCTURE (COMPOSITION);

DISCONTINUITIES; MECHANICS OF DEFORMABLE SOLIDS; THERMO-MECHANICS; VARIATIONAL FORMULATION; VIRTUAL POWER;

CONTINUUM MECHANICS;

EID: 84879686619     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-011-0196-7     Document Type: Review

References (52)

1. Mach, E.: The science of mechanics; A critical and historical account of its Development, Open Court, Chicago (1911; Paperback 1988) (Original German edition: F.A.Brockhaus, Leipzig, 1883). pp. 59-88, 420-432 in the English text
2. Dugas, R.: A history of mechanics, Dover reprint, New York (1988; Original edition: Editions du Griffon, Neuchatel, Switzerland, 1955; French and English versions were published simultaneously)
3. Timoshenko, S.P.: History of strength of materials, Dover, New York (1983; original edition, McGraw-Hill, New York, 1953)
4. Budo, A.: Theoretische Mechanik, VEB Deutscher Verlag der Wissenschaften, Berlin (DDR), 4th German edition, (1967; original Hungarian edition, Budapest, 1953)
5. Szabo I.: Geschichte der mechanischen Prinzipien, 3rd edn. Birkhäuser, Basel (1987)
6. Crowe M.J.: Mechanics from Aristotle to Einstein. Green Lyon Press, Santa Fe (2007)
7. Maugin G.A.: The method of virtual power in continuum mechanics: application to coupled fields. Acta Mech. 35/1, 1-70 (1980)
8. Germain P.: La méthode des puissances virtuelles en mécanique des milieux continus, Première partie: théorie du second gradient. J. de Mécanique (Paris) 12, 235-274 (1973)
9. Germain P.: The method of virtual power in continuum mechanics-II: microstructure. SIAM J. Appl. Math. 25, 556-575 (1973)
10. Truesdell, C.A., Toupin, R.A.: The classical theory of fields. In: S. Flügge (ed) Handbuch der Physik, Bd.III/1, Springer, Berlin (1960)
11. Germain P.: Mécanique des milieux continus. Masson Editeurs, Paris (1962)
12. Germain, P.: Contribution à l'étude des milieux micropolaires et micromorphiques. In: Omaggio a Carlo Ferrari, Levretto e Bella, Torino, pp. 273-297 (1974)
13. Germain P.:: Duality and convection in continuum mechanics. In: Fichera, D. (eds) Trends in Applications of Pure Mathematics to Mechanics, pp. 107-128. Pitman, London (1976)
14. Maugin G.A.: Material Inhomogeneities in Elasticity. Chapman and Hall, London (1993)
15. Maugin G.A.: Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam (1988)
16. Dell'Isola F., Seppecher P.: The relationship between edge contact forces, double forces and intersticial working allowed by the principle of virtual power. C.R. Acad. Sci. Paris II b 321, 303-308 (1995)
17. Noll W., Virga E.G.: On edge interactions and surface tension. Arch. Rat. Mech. Anal. 111, 1-31 (1990)
18. Gurtin M.E., Mizel V.J., Williams W.O.: A note on Cauchy's stress theorem. J. Math. Anal. Appl. 22, 398-401 (1968)
19. Mindlin R.D., Eshel N.N.: On the first strain gradient theories in linear elasticity. Int. J. Solids Struct. 4, 109-124 (1968)
20. Mindlin R.D., Tiersten H.F.: Effects of couple stresses in linear elasticity. Arch. Rat. Mech. Anal. 11, 415-448 (1962)
21. Maugin G.A.: What do we understand by "generalized continuum mechanics"?. In: Maugin, G.A., Metrikine, A.V., Erofeyev, E.V. (eds) Mechanics of Generalized Continua: A Hundred Years After the Cosserats, pp. 3-13. Springer, New York (2010)
22. Maugin, G.A.: Nonlocal theories or gradient-type theories. A matter of convenience? Arch. Mech. (Poland) 31, 15-26 (1979) [presented at Euromech Colloquium held in Warsaw, 1977]
23. Le Roux, J.: Etude géométrique de la torsion et de la flexion, dans les déformations infinitésimales d'un milieu continu. Ann. Ecole Norm. Sup. 28, 523-579 (1911) (also, Recherches sur la géométrie des déformations finies, ibid, 30, 193-245, 1913)
24. Casal P.: La théorie du second gradient et la capillarité. C.R. Acad. Sci. Paris 274A, 1075-1078 (1972)
25. Cosserat, E. and F., Théorie des corps déformables. Hermann Editeurs, Paris (1909; Reprint, Editions Gabay, Paris, 2008)
26. Eringen A.C.: Theory of micropolar fluids. J. Math. Mech. 16, 1-18 (1966)
27. Eringen A.C.: Microcontinuum Field Theories I: Foundations and Solids. Springer, New York (1999)
28. Eringen A.C.: Theory of micropolar elasticity. In: Liebowitz, H. (ed.) Fracture: A Treatise, vol. II, pp. 621-729. Academic Press, New York (1968)
29. Maugin G.A.: Sur la dynamique des milieux déformables avec spin magnétique- Théorie classique. J. Mécanique (Paris) 13, 75-96 (1974)
30. Maugin G.A.: A continuum theory of deformable ferrimagnetic bodies-I-field equations. J. Math. Phys. (USA) 17, 1727-1738 (1976)
31. Collet B., Maugin G.A.: Couplage magnétoélastique de surface dans les milieux ferromagnétiques. C.R. Acad. Sci. Paris 280A, 1641-1644 (1975)
32. Daher N., Maugin G.A.: The method of virtual power in continuum mechanics: application to media presenting singular surfaces and interfaces. Acta Mech. 60, 217-240 (1986)
33. Daher N., Maugin G.A.: Virtual power and thermodynamics for electromagnetic continua with interfaces. J. Math. Phys. (USA) 27, 3022-3035 (1986)
34. Daher N., Maugin G.A.: Deformable semiconductors with interfaces: basic equations. Int. J. Eng. Sci. 25, 1093-1129 (1987)
35. Truesdell C.A.: Rational Thermodynamics. Springer, New York (1984)
36. Quiligotti S., Maugin G.A., dell'Isola F.: An Eshelbian approach to the nonlinear mechanics of constrained solid-fluid mixtures. Acta Mech. 160, 45-60 (2003)
37. Kestin J.: Local equilibrium formalism applied to mechanics of solids. Int. J. Solids Struct. 29, 1827-1836 (1992)
38. Maugin G.A.: The thermomechanics of nonlinear irreversible behaviours. World Scientific, New Jersey (1999)
39. Frémond M., Nedjar B.: Endommagement et principe des puissances virtuelles. C.R. Acad. Sci. Paris II-317, 857-864 (1993)
40. Maugin G.A.: On the thermomechanics of continuous media with diffusion and /or weak nonlocality. Arch Appl. Mech. 75, 723-738 (2006)
41. Gold'enweizer A.L.: Methods for justifying and refining the theory of shells. Appl. Math. Mech. (P.M.M.) 32, 704-718 (1968)
42. Ciarlet P.G., Destuynder P.: A justification of a nonlinear model in plate theory. Comput. Methods Appl. Mech. Eng. 17/18, 227-258 (1979)
43. Destuynder, P.: On a justification of models of plates and shells by asymptotic methods (in French). State Doctoral Thesis, University of Paris 6, Paris (1980)
44. q, Rio de Janeiro, Brazil (July 1982) (unfortunately not published in any other form)
45. Touratier M.: An efficient standard plate theory. Int. J. Eng. Sci. 29, 901-916 (1991)
46. Touratier M., Maugin G.A.: Heterogeneous elastic wave guides of rectangular cross section. J. Acoust. Soc. Am. 78, 1806-1825 (1985)
47. Salençon, J.: Mécanique des milieux continus, Tome I: Concepts généraux, Editions de l'Ecole Polytechnique, Palaiseau (2001)
48. Nayroles B.: Opérations algébriques en mécanique des structures. C.R. Acad. Sci. Paris 273A, 1075-1078 (1971)
49. d'Alembert, J. Le Rond: Traité de dynamique, 1st edn, Paris (1743) [Reprinted by Gauthier-Villars Publishers, in two volumes, Paris, 1925; also Fac-simile Reprint by Editions Gabay, Paris, 1998]
50. Maugin, G.A.: A relativistic version of the principle of virtual power [K.Kondo Anniversary volume]. Int. J. Eng. Sci. 19, 1719-1730 (1981)
51. Maugin, G.A., Paul Germain: (1920-2009), L'Archicube (Bulletin de l'Association des Anciens élèves de l'Ecole Normale Supérieure de Paris), 7bis, Special issue, pp. 126-129, Février 2010
52. Maugin, G.A., Drouot, R., Sidoroff, F. (eds.): Continuum Thermomechanics: The Art and Science of Modelling Material Behaviour (Paul Germain's Anniversary Volume), Kluwer Academic Publishers, Dordrecht, The Netherlands (2000; Contribution by Paul Germain: "My discovery of Mechanics", pp. 1-24, English text by Eleni Maugin)