An invariance argument is presented that yields the constitutive splitting of the total energy into an internal and a kinetic part, as well as a representation of the latter and the inertial forces in terms of one and the same mass tensor.
Beatty M. F.,On the foundation principles of general classical mechanics, Arch. Rational Mech. Anal.,27 (1967), pp. 264–273.
Coleman B. D. -W. Noll,The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal.,13 (1963), pp. 167–178.
Capriz G. -P. Podio-Guidugli,Structured continua from a Lagrangian point of view, Ann. Mat. Pura Appl. (IV),135 (1983), pp. 1–25.
Capriz G. -P. Podio-Guidugli -W. O. Williams,On balance equations for materials with affine structure, Meccanica,17 (1982), pp. 80–84.
DeSimone A. - P.Podio-Guidugli,On the continuum theory of deformable ferromagnetic solids, Arch. Rational Mech. Anal. (1996), in the press.
Ericksen J. L.,Conservation laws for liquid crystals, Trans. Soc. Rheol.,5 (1961), pp. 23–34.
Green A. E. -R. S. Rivlin,On Cauchy's equations of motion, Z. Angew. Math. Phys.,15 (1964a), pp. 290–292.
Green A. E. -R. S. Rivlin,Simple force and stress multipoles, Arch. Rational Mech. Anal.,16 (1964b), pp. 325–353.
Gurtin M. E.,An Introduction to Continuum Mechanics, Academic Press (1981).
Gurtin M. E. -P. Podio-Guidugli,The thermodynamics of constrained materials, Arch. Rational Mech. Anal.,51 (1973), pp. 192–208.
Gurtin M. E. -W. O. Williams,On the first law of thermodynamics, Arch. Rational Mech. Anal.,42 (1971), pp. 77–92.
Lucchesi M. -D. R. Owen -P. Podio-Guidugli,Materials with elastic range: a theory with a view toward applications, Part III: Approximate constitutive relations, Arch. Rational Mech. Anal,117 (1992), pp. 53–96.
Marsden J. E. - T. J. R.Hughes,Mathematical Foundations of Elasticity, Prentice-Hall (1983).
Naghdi P. M.,The theory of shells and plates, pp. 425–640of Mechanics of Solids II,Handbuch der Physik,S. Flügge Ed., Vol. VIa/2, Springer-Verlag, Berlin, Heidelberg, New York (1972).
Noll W.,La mécanique classique, basée sur un axiome de objectivité, pp. 47–56 ofLa Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles (Colloque International, Paris, 1959), Gauthier-Villars, Paris (1963) (reprinted inNoll's Selecta (1974)).
Noll W.,The Foundations of Mechanics and Thermodynamics, Springer-Verlag (1974).
Serrin J.,On the axioms of classical mechanics, unpublished (Sept. 1974).
Serrin J.,The equations of continuum mechanics as a consequence of invariance and thermodynamical principles, Lecture at the Conference on Nonlinear Analysis and Partial Differential Equations, Rutgers University, May 1990.
Serrin J.,The equations of continuum mechanics as a consequence of group invariance, Lecture at the Conference on Advances in Modern Continuum Dynamics, Isola d'Elba, June 1991.
Serrin J.,Space, Time, and Energy, Lectio Doctoralis at the Universitá di Ferrara, 29 October 1992.
Šilhavý M.,On the concepts of mass and linear momentum in Galilean thermodynamics, Czech. J. Phys., B37 (1987), pp. 133–157.
Šilhavý M.,Mass, internal energy, and Cauchy's equations in frame indifferent thermodynamics, Arch. Rational Mech. Anal.,107 (1989), pp. 1–22.
Šilhavý M.,Energy principle and the equations of motion in Galilean thermodynamics, Czech. J. Phys.,42 (1992), pp. 363–374.
Simo J. C. -J. E. Marsden,On the rotated stress tensor and the material version of the Doyle-Ericksen formula, Arch. Rational Mech. Anal.,86 (1984), pp. 213–231.
Truesdell C.,Rational Thermodynamics, 2nd ed., Springer-Verlag, New York, Berlin, Heidelberg, Tokyo (1984).
Truesdell C.,A First Course in Rational Continuum Mechanics, Vol. 1, 2nd ed., Academic Press (1991).
Truesdell C. - W.Noll,The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol. III, S.Flügge Ed., Springer-Verlag (1965).
Williams W. O., Review ofContinua with Microstructure, by G.Capriz, Springer-Verlag, New York (1989); SIAM Review, 33,1 (1991), pp. 161–163.
Dedicated to Professor Walter Noll on the occasion of his retirement from teaching.
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Podio-Guidugli, P. Inertia and invariance. Annali di Matematica pura ed applicata 172, 103–124 (1997). https://doi.org/10.1007/BF01782609
- Total Energy
- Inertial Force
- Kinetic Part
- Mass Tensor
- Invariance Argument