Variational Principles of Continuum Mechanics

By V. Berdichevsky. 2009

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Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, methodology): “gration-by-parts techniques were introduced to us by Seppecher [139]. They are developed in the framework of Levi-Civita absolute tensor calculus, however it is clear that the sources of Berdichevsky [9] systematically employed these techniques. With their help, the expression (16) is transformed in”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, methodology): “eference conﬁguration: in these works there is no trace of more generalized models of the type introduced by the Cosserats [21]. However the spirit of Piola’s variational formulation (see, e.g., [6], [7], [25], [52], [53], [60], [74], [137], [138]) and his methods for introducing generalized stress ”