Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F20%3A00341259" target="_blank" >RIV/68407700:21110/20:00341259 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1186/s40323-020-00152-7" target="_blank" >https://doi.org/10.1186/s40323-020-00152-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1186/s40323-020-00152-7" target="_blank" >10.1186/s40323-020-00152-7</a>

Result language

angličtina

Original language name

Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Original language description

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for higher-order integration rules. Because evaluation of a constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency of the micromorphic scheme can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from expensive mass-matrix to a cheaper stiffness-matrix equivalent are outlined first. An efficient one-point integration quadrilateral element is then introduced and a proper hourglass stabilization is discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules, whereas computational cost decreases proportionally to the reduction in the number of quadrature points used.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

20501 - Materials engineering

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2020

Confidentiality

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

Name of the periodical

Advanced Modeling and Simulation in Engineering Sciences

ISSN

2213-7467

e-ISSN

2213-7467

Volume of the periodical

7

Issue of the periodical within the volume

1

Country of publishing house

GB - UNITED KINGDOM

Number of pages

17

Pages from-to

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UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85083388400