A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials
Original language description
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.
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
<a href="/en/project/GX19-26143X" target="_blank" >GX19-26143X: Non-periodic pattern-forming metamaterials: Modular design and fabrication</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computer Methods in Applied Mechanics and Engineering
ISSN
0045-7825
e-ISSN
1879-2138
Volume of the periodical
372
Issue of the periodical within the volume
113333
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
25
Pages from-to
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UT code for WoS article
000592532900007
EID of the result in the Scopus database
2-s2.0-85090117223