A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F20%3A00344067" target="_blank" >RIV/68407700:21110/20:00344067 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.cma.2020.113333" target="_blank" >https://doi.org/10.1016/j.cma.2020.113333</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2020.113333" target="_blank" >10.1016/j.cma.2020.113333</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials

Popis výsledku v původním jazyce

Mechanical metamaterials feature microstructures designed to exhibit exotic effective behaviour such as negative Poisson’s ratio or negative compressibility. Such a specific response is often achieved through instability-induced transformations of the underlying periodic microstructure. Due to a strong kinematic coupling of individual repeating microstructural cells, non-local behaviour and size effects emerge, which cannot easily be captured by classical homogenization schemes. For efficient numerical predictions of macroscale engineering applications, a micromorphic computational homogenization scheme has recently been developed by the authors. Although this framework is in principle capable of accounting for spatial and temporal interactions between individual patterning modes, its implementation relied on a gradient-based quasi-Newton solution technique, which is suboptimal because (i) it has sub-quadratic convergence, and (ii) the absence of Hessians does not allow for proper bifurcation analyses. To address these serious limitations, a full Newton method, entailing all derivations and definitions of the tangent operators, is provided in detail in this paper. Analytical expressions for the first and second variation of the total potential energy are given, and the complete algorithm is listed. The developed methodology is demonstrated with two examples in which a competition between local and global buckling exists and where multiple patterning modes emerge. The numerical results indicate that local to global buckling transition can be predicted within a relative error of 6% in terms of the applied strains. The expected pattern combinations are triggered even for the case of multiple patterns.

Název v anglickém jazyce

A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials

Popis výsledku anglicky

Mechanical metamaterials feature microstructures designed to exhibit exotic effective behaviour such as negative Poisson’s ratio or negative compressibility. Such a specific response is often achieved through instability-induced transformations of the underlying periodic microstructure. Due to a strong kinematic coupling of individual repeating microstructural cells, non-local behaviour and size effects emerge, which cannot easily be captured by classical homogenization schemes. For efficient numerical predictions of macroscale engineering applications, a micromorphic computational homogenization scheme has recently been developed by the authors. Although this framework is in principle capable of accounting for spatial and temporal interactions between individual patterning modes, its implementation relied on a gradient-based quasi-Newton solution technique, which is suboptimal because (i) it has sub-quadratic convergence, and (ii) the absence of Hessians does not allow for proper bifurcation analyses. To address these serious limitations, a full Newton method, entailing all derivations and definitions of the tangent operators, is provided in detail in this paper. Analytical expressions for the first and second variation of the total potential energy are given, and the complete algorithm is listed. The developed methodology is demonstrated with two examples in which a competition between local and global buckling exists and where multiple patterning modes emerge. The numerical results indicate that local to global buckling transition can be predicted within a relative error of 6% in terms of the applied strains. The expected pattern combinations are triggered even for the case of multiple patterns.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GX19-26143X" target="_blank" >GX19-26143X: Neperiodické materiály vykazující strukturované deformace: Modulární návrh a výroba</a><br>

Návaznosti

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

Rok uplatnění

2020

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

372

Číslo periodika v rámci svazku

113333

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

—

Kód UT WoS článku

000592532900007

EID výsledku v databázi Scopus

2-s2.0-85090117223