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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/25:10509224

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF22-00863K" target="_blank" >GF22-00863K: Řiditelné metamateriály a chytré struktury: Nelineární problémy, modelování a experimenty</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics and Mechanics of Solids

ISSN

1081-2865

e-ISSN

1741-3028

Svazek periodika

30

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

37

Strana od-do

2365-2401

Kód UT WoS článku

001429085500001

EID výsledku v databázi Scopus

2-s2.0-105000019524