Variational principles are a powerful tool also for formulating field theories

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Dell'Isola, Francesco; Placidi, Luca;
(2012)
  • Publisher: HAL CCSD
  • Subject: [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] | [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] | [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] | [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]

Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for s... View more
  • References (22)
    22 references, page 1 of 3

    [1] Arnold, V.I., Mathematical Methods of Classical Mechanics, Springer, 2nd edition, May 16, 1989.

    [2] Benvenuto, E., La scienza delle costruzioni e il suo sviluppo storico, Sansoni, Firenze, 1981.

    [3] Berdichevsky V., Variational Principles of Continuum Mechanics, Springer, 2009.

    [4] Bourdin, B., Francfort, G.A., Marigo, J.-J., The variational approach to fracture, J. Elasticity, 91, 1-3, 1-148, 2008. (The paper also appeared as a Springer book: ISBN: 978-1-4020-6394-7).

    [5] Colonnetti, G., Scienza delle costruzioni, Torino, Edizioni scientifiche Einaudi, 3rd ed., 1953-57.

    [6] Cosserat, E., Cosserat, F., Sur la Th´eorie des Corps D´eformables, Herman, Paris, 1909.

    [7] dell'Isola, F., Seppecher, P., The relationship between edge contact forces, double force and interstitial working allowed by the principle of virtual power, Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie, vol. 321, pp. 303-308, 1995.

    [8] dell'Isola, F., Seppecher, P., Edge Contact Forces and Quasi-Balanced Power, Meccanica, vol. 32, pp. 33-52, 1997.

    [9] dell'Isola, F., Madeo, A., Seppecher, P., Boundary Conditions in Porous Media: A Variational Approach, Int. Journal of Solids and Structures, Vol. 46, 3150-3164, 2009.

    [10] dell'Isola, F., Madeo, A., Seppecher, P., “Beyond Euler-Cauchy continua”. In this book.

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