Visco-elastodynamics at large strains Eulerian
From MaRDI portal
Publication:6359431
DOI10.1007/S00033-022-01686-ZarXiv2102.00261MaRDI QIDQ6359431
Publication date: 30 January 2021
Abstract: Isothermal visco-elastodynamics in the Kelvin-Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted. The model involves a nonlinear 2nd-grade nonsimple (multipolar) viscosity so that the velocity field is well regular. To simplify analytical arguments, volume variations of the solid material are assumed to be only rather small so that the mass density is constant, exploiting the concept of semi-compressible materials. Existence of weak solutions is proved by using the Galerkin method combined with a suitable regularization, using nontrivial results about transport by smooth velocity fields.
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Nonlinear elasticity (74B20) Viscoelastic fluids (76A10) Nonsimple materials (74A30) Weak solutions to PDEs (35D30) Existence of solutions of dynamical problems in solid mechanics (74H20) PDEs in connection with mechanics of deformable solids (35Q74)
This page was built for publication: Visco-elastodynamics at large strains Eulerian
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6359431)
