Dynamic perfect plasticity and damage in viscoelastic solids

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F19%3A00517342" target="_blank" >RIV/61388998:_____/19:00517342 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/19:10403459

Výsledek na webu

<a href="https://onlinelibrary.wiley.com/doi/10.1002/zamm.201800161" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/zamm.201800161</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/zamm.201800161" target="_blank" >10.1002/zamm.201800161</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dynamic perfect plasticity and damage in viscoelastic solids

Popis výsledku v původním jazyce

In this paper we analyze an isothermal and isotropic model for viscoelastic media combining linearized perfect plasticity (allowing for concentration of plastic strain and development of shear bands) and damage effects in a dynamic setting. The interplay between the viscoelastic rheology with inertia, elasto‐plasticity, and unidirectional rate‐dependent incomplete damage affecting both the elastic and viscous response, as well as the plastic yield stress, is rigorously characterized by showing existence of weak solutions to the constitutive and balance equations of the model. The analysis relies on the notions of plastic‐strain measures and bounded‐deformation displacements, on sophisticated time‐regularity estimates to establish a duality between acceleration and velocity of the elastic displacement, on the theory of rate‐independent processes for the energy conservation in the dynamical‐plastic part, and on the proof of the strong convergence of the elastic strains. Existence of suitably defined weak solutions (even conserving energy) is proved rather constructively by using a staggered two‐step time discretization scheme.

Název v anglickém jazyce

Dynamic perfect plasticity and damage in viscoelastic solids

Popis výsledku anglicky

In this paper we analyze an isothermal and isotropic model for viscoelastic media combining linearized perfect plasticity (allowing for concentration of plastic strain and development of shear bands) and damage effects in a dynamic setting. The interplay between the viscoelastic rheology with inertia, elasto‐plasticity, and unidirectional rate‐dependent incomplete damage affecting both the elastic and viscous response, as well as the plastic yield stress, is rigorously characterized by showing existence of weak solutions to the constitutive and balance equations of the model. The analysis relies on the notions of plastic‐strain measures and bounded‐deformation displacements, on sophisticated time‐regularity estimates to establish a duality between acceleration and velocity of the elastic displacement, on the theory of rate‐independent processes for the energy conservation in the dynamical‐plastic part, and on the proof of the strong convergence of the elastic strains. Existence of suitably defined weak solutions (even conserving energy) is proved rather constructively by using a staggered two‐step time discretization scheme.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA18-03834S" target="_blank" >GA18-03834S: Jevy lokalizace v materiálech s tvarovou pamětí: experimenty a modelování</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik

ISSN

0044-2267

e-ISSN

—

Svazek periodika

99

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

27

Strana od-do

UNSP e201800161

Kód UT WoS článku

000474796200002

EID výsledku v databázi Scopus

2-s2.0-85067379945