Reduced variational formulations in free boundary continuum mechanics
In free-boundary continuum mechanics, the authors apply the Lagrangian reduction approach, allowing a better use of the material and spatial symmetries of the studied systems. The results of the article are achieved by implementing the Euler-Poincaré reduction for a semidirect product involving the diffeomorphism group of the fluids domain in compressible hydrodynamics. Here both the constrained variational principle and the equations of motion are presented. But the Euler-Poincaré reduction theory is not applied in nonlinear elasticity problems, where the constrained variational principles together with the equations of motion are deduced from the material representation, both in convective and spatial formulation. The same approach of Lagrangian reduction is carried out for free-boundary compressible fluids with surface tension allowing to deduce the equations of motion and their associated constrained variational principles in convective and spatial representation. Lagrangian reduction is also acceptable for general continua, in particularl for fluid-solid interaction problems. Here the extension of the notions of material and spatial symmetries allow to deduce the constrained variational principles in pure spatial or convective variables and to derive the equations of motion in convective and spatial representations.
scientific article; zbMATH DE number 6100219
scientific article