We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope with possible global self-interpenetration, yielding thus a certain justification of most of engineering calculations which ignore these effects in the analysis of elastic structures. These models necessarily combine Lagrangian (material) description with Eulerian (actual) evolving configuration evolving in time. Dynamical problems are studied by adopting the concept of nonlocal nonsimple materials, applying the change of variables formula for Lipschitz-continuous mappings, and relying on the positivity of the determinant of the deformation gradient thanks to a result by Healey and Kroemer.

Roubicek, T., Tomassetti, G. (2020). Dynamics of charged elastic bodies under diffusion at large strains. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., 25(4), 1415-1437 [10.3934/dcdsb.2019234].

Dynamics of charged elastic bodies under diffusion at large strains

Giuseppe Tomassetti
2020-01-01

Abstract

We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope with possible global self-interpenetration, yielding thus a certain justification of most of engineering calculations which ignore these effects in the analysis of elastic structures. These models necessarily combine Lagrangian (material) description with Eulerian (actual) evolving configuration evolving in time. Dynamical problems are studied by adopting the concept of nonlocal nonsimple materials, applying the change of variables formula for Lipschitz-continuous mappings, and relying on the positivity of the determinant of the deformation gradient thanks to a result by Healey and Kroemer.
2020
Roubicek, T., Tomassetti, G. (2020). Dynamics of charged elastic bodies under diffusion at large strains. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., 25(4), 1415-1437 [10.3934/dcdsb.2019234].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/360204
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