Time discretization in visco-elastodynamics at large displacements and strains in the Eulerian frame

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F25%3A00644405" target="_blank" >RIV/61388998:_____/25:00644405 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/25:10509224
Result on the web
<a href="https://journals.sagepub.com/doi/10.1177/10812865241313046" target="_blank" >https://journals.sagepub.com/doi/10.1177/10812865241313046</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1177/10812865241313046" target="_blank" >10.1177/10812865241313046</a>

Result language
angličtina
Original language name
Time discretization in visco-elastodynamics at large displacements and strains in the Eulerian frame
Original language description
The fully implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e., in the actual deforming configuration, formulated fully in terms of rates. The Kelvin-Voigt rheology or also, in the deviatoric part, the Jeffreys rheology are considered. Both a linearized convective model at large displacements with a convex stored energy and the fully nonlinear large strain variant with a (possibly generalized) polyconvex stored energy are considered. The time-discrete suitably regularized schemes are devised for both cases. The numerical stability and, considering the multipolar 2nd-grade viscosity, also convergence towards weak solutions are proved, exploiting the convexity of the kinetic energy when written in terms of linear momentum instead of velocity. In the fully nonlinear case, the examples of neo-Hookean and Mooney-Rivlin materials are presented. A comparison with models of viscoelastic barotropic fluids is also made.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GF22-00863K" target="_blank" >GF22-00863K: Controllable metamaterials and smart structures: Nonlinear problems, modelling and experiments</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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