Abstract
Using the concept of symplectic subdifferential, we propose a modification of the Hamiltonian formalism which can be used for dissipative systems. The formalism is first illustrated through an application of the standard inelasticity in small strains. Some hints concerning possible extensions to non-standard plasticity and finite strains are then given. Finally, we show also how the dissipative transition between macrostates can be viewed as an optimal transportation problem.
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Aknowledgement
This work was performed thanks to the international cooperation project Dissipative Dynamical Systems by Geometrical and Variational Methods and Application to Viscoplastic Structures Subjected to Shock Waves (DDGV) supported by the Agence Nationale de la Recherche (ANR) and the Deutsche Forchungsgemeinschaft (DFG).
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Oueslati, A., Nguyen, A.D., de Saxcé, G. (2017). A Symplectic Minimum Variational Principle for Dissipative Dynamical Systems. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_42
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DOI: https://doi.org/10.1007/978-3-319-68445-1_42
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