eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F17%3A00312057" target="_blank" >RIV/68407700:21110/17:00312057 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985556:_____/17:00475349

Výsledek na webu

<a href="http://arxiv.org/abs/1612.03876" target="_blank" >http://arxiv.org/abs/1612.03876</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2017.03.042" target="_blank" >10.1016/j.cma.2017.03.042</a>

Jazyk výsledku

angličtina

Název v původním jazyce

eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation

Popis výsledku v původním jazyce

Lattice networks with dissipative interactions are often employed to analyse materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully -resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.

Název v anglickém jazyce

eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation

Popis výsledku anglicky

Lattice networks with dissipative interactions are often employed to analyse materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully -resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20302 - Applied mechanics

Projekt

<a href="/cs/project/GA14-00420S" target="_blank" >GA14-00420S: Kvazikontuální metody pro diskrétní disipativní soustavy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

e-ISSN

1879-2138

Svazek periodika

320

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

24

Strana od-do

769-792

Kód UT WoS článku

000402212200030

EID výsledku v databázi Scopus

2-s2.0-85018567758