The peridynamic stress tensors and the non-local to local passage
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The peridynamic stress tensors and the non-local to local passage
Original language description
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' the 1st Piola-Kirchhoff stress tensor. Throughout the whole paper we suppose that the deformation is sufficiently regular.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ZAMM Zeitschrift für Angewandte Mathematik und Mechanik
ISSN
0044-2267
e-ISSN
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Volume of the periodical
99
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
13
Pages from-to
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UT code for WoS article
000477087700005
EID of the result in the Scopus database
2-s2.0-85062947567