The peridynamic stress tensors and the non-local to local passage

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403590" target="_blank" >RIV/00216208:11320/19:10403590 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ATNP7~s51X" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ATNP7~s51X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/zamm.201800010" target="_blank" >10.1002/zamm.201800010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The peridynamic stress tensors and the non-local to local passage

Popis výsledku v původním jazyce

Motivated by earlier works by S.A. Silling and R.B. I,ehoucq, we re-examine the notion of stress and force flux in peridynamics - a useful connection to measurable quantities and classical view of continuum mechanics. Based on the idea of traction we define two new peridynamic stress tensors P-y and P which stand, respectively, for analogues of the Cauchy and 1st Piola-Kirchhoff stress tensors from classical elasticity, We show that the tensor P differs from the earlier defined peridynainic stress tensor v; though their divergence is equal. We address the question of symmetry of the tensor P-y which proves to be symmetric in case of bond-based peridynaniics; as opposed to the inverse Piola transform of v (corresponding to the analogue of Cauchy stress tensor) which fails to be symmetric in general. We also derive a gen eral formula of the force-flux in peridynamics and compute the limit of P for vanishing non-locality, denoted by P-0. For the sake of brevity we stick to bond-based peridynamic in our calculations. We show that this tensor P-0 surprisingly coincides with the collapsed tensor vo, the limit of the original tensor v. At the end, using this flux formula, we suggest an explanation why the collapsed tensor P-0 (and hence vo) can be indeed identified with&apos; the 1st Piola-Kirchhoff stress tensor. Throughout the whole paper we suppose that the deformation is sufficiently regular.

Název v anglickém jazyce

The peridynamic stress tensors and the non-local to local passage

Popis výsledku anglicky

Motivated by earlier works by S.A. Silling and R.B. I,ehoucq, we re-examine the notion of stress and force flux in peridynamics - a useful connection to measurable quantities and classical view of continuum mechanics. Based on the idea of traction we define two new peridynamic stress tensors P-y and P which stand, respectively, for analogues of the Cauchy and 1st Piola-Kirchhoff stress tensors from classical elasticity, We show that the tensor P differs from the earlier defined peridynainic stress tensor v; though their divergence is equal. We address the question of symmetry of the tensor P-y which proves to be symmetric in case of bond-based peridynaniics; as opposed to the inverse Piola transform of v (corresponding to the analogue of Cauchy stress tensor) which fails to be symmetric in general. We also derive a gen eral formula of the force-flux in peridynamics and compute the limit of P for vanishing non-locality, denoted by P-0. For the sake of brevity we stick to bond-based peridynamic in our calculations. We show that this tensor P-0 surprisingly coincides with the collapsed tensor vo, the limit of the original tensor v. At the end, using this flux formula, we suggest an explanation why the collapsed tensor P-0 (and hence vo) can be indeed identified with&apos; the 1st Piola-Kirchhoff stress tensor. Throughout the whole paper we suppose that the deformation is sufficiently regular.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>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 für Angewandte Mathematik und Mechanik

ISSN

0044-2267

e-ISSN

—

Svazek periodika

99

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

—

Kód UT WoS článku

000477087700005

EID výsledku v databázi Scopus

2-s2.0-85062947567