Extended quasicontinuum methodology for highly heterogeneous discrete systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F24%3A00375224" target="_blank" >RIV/68407700:21110/24:00375224 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1002/nme.7415" target="_blank" >https://doi.org/10.1002/nme.7415</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/nme.7415" target="_blank" >10.1002/nme.7415</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extended quasicontinuum methodology for highly heterogeneous discrete systems

Popis výsledku v původním jazyce

Lattice networks are indispensable to study heterogeneous materials such as concrete or rock as well as textiles and woven fabrics. Due to the discrete character of lattices, they quickly become computationally intensive. The QuasiContinuum (QC) Method resolves this challenge by interpolating the displacement of the underlying lattice with a coarser finite element mesh and sampling strategies to accelerate the assembly of the resulting system of governing equations. In lattices with complex heterogeneous microstructures with a high number of randomly shaped inclusions the QC leads to an almost fully-resolved system due to the many interfaces. In the present study the QC Method is expanded with enrichment strategies from the eXtended Finite Element Method (XFEM) to resolve material interfaces using nonconforming meshes. The goal of this contribution is to bridge this gap and improve the computational efficiency of the method. To this end, four different enrichment strategies are compared in terms of their accuracy and convergence behavior. These include the Heaviside, absolute value, modified absolute value and the corrected XFEM enrichment. It is shown that the Heaviside enrichment is the most accurate and straightforward to implement. A first-order interaction based summation rule is applied and adapted for the extended QC for elements intersected by a material interface to complement the Heaviside enrichment. The developed methodology is demonstrated by three numerical examples in comparison with the standard QC and the full solution. The extended QC is also able to predict the results with 5% error compared to the full solution, while employing almost one order of magnitude fewer degrees of freedom than the standard QC and even more compared to the fully-resolved system.

Název v anglickém jazyce

Extended quasicontinuum methodology for highly heterogeneous discrete systems

Popis výsledku anglicky

Lattice networks are indispensable to study heterogeneous materials such as concrete or rock as well as textiles and woven fabrics. Due to the discrete character of lattices, they quickly become computationally intensive. The QuasiContinuum (QC) Method resolves this challenge by interpolating the displacement of the underlying lattice with a coarser finite element mesh and sampling strategies to accelerate the assembly of the resulting system of governing equations. In lattices with complex heterogeneous microstructures with a high number of randomly shaped inclusions the QC leads to an almost fully-resolved system due to the many interfaces. In the present study the QC Method is expanded with enrichment strategies from the eXtended Finite Element Method (XFEM) to resolve material interfaces using nonconforming meshes. The goal of this contribution is to bridge this gap and improve the computational efficiency of the method. To this end, four different enrichment strategies are compared in terms of their accuracy and convergence behavior. These include the Heaviside, absolute value, modified absolute value and the corrected XFEM enrichment. It is shown that the Heaviside enrichment is the most accurate and straightforward to implement. A first-order interaction based summation rule is applied and adapted for the extended QC for elements intersected by a material interface to complement the Heaviside enrichment. The developed methodology is demonstrated by three numerical examples in comparison with the standard QC and the full solution. The extended QC is also able to predict the results with 5% error compared to the full solution, while employing almost one order of magnitude fewer degrees of freedom than the standard QC and even more compared to the fully-resolved system.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20501 - Materials engineering

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

International Journal for Numerical Methods in Engineering

ISSN

0029-5981

e-ISSN

1097-0207

Svazek periodika

125

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

—

Kód UT WoS článku

001129503400001

EID výsledku v databázi Scopus

2-s2.0-85180841386