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Intrinsic mixed-dimensional beam-shell-solid couplings in linear Cosserat continua via tangential differential calculus.

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Title: Intrinsic mixed-dimensional beam-shell-solid couplings in linear Cosserat continua via tangential differential calculus.
Authors: Sky, Adam1 (AUTHOR) adam.sky@uni.lu, Hale, Jack S.1 (AUTHOR) jack.hale@uni.lu, Zilian, Andreas1 (AUTHOR) andreas.zilian@uni.lu, Bordas, Stéphane P.A.1 (AUTHOR) stephane.bordas@alum.northwestern.edu, Neff, Patrizio2 (AUTHOR) patrizio.neff@uni-due.de
Source: Computer Methods in Applied Mechanics & Engineering. Dec2024:Part A, Vol. 432, pN.PAG-N.PAG. 1p.
Subjects: Shell Oil Co., Differential calculus, Finite element method, Degrees of freedom, Graphite, Silver
Abstract: We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the model to lower dimensional domains leaves its fundamental degrees of freedom intact. Consequently, the degrees of freedom intrinsically agree even at the interface with a domain of a different dimensionality. Thus, this approach circumvents the need for intermediate finite elements or mortar methods. We introduce the derivations of all models of various dimensions using tangential differential calculus. The coupling itself is then achieved by defining a mixed-dimensional action functional with consistent Sobolev trace operators. Finally, we present numerical examples involving a three-dimensional silicone-rubber block reinforced with a curved graphite shell on its lower surface, a three-dimensional silver block reinforced with a graphite plate and beams, and lastly, intersecting silver shells reinforced with graphite beams. • The linear Cosserat micropolar model and its limit case for homogeneous Cauchy materia. • Derivations of Cosserat shell and beam models using tangential differential calculus. • A mixed-dimensional action functional via Sobolev trace operators for model-coupling. • Examination of the corresponding finite element spaces on codimensional domains. • Numerical examples to validate the approach and demonstrate its flexibility. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the model to lower dimensional domains leaves its fundamental degrees of freedom intact. Consequently, the degrees of freedom intrinsically agree even at the interface with a domain of a different dimensionality. Thus, this approach circumvents the need for intermediate finite elements or mortar methods. We introduce the derivations of all models of various dimensions using tangential differential calculus. The coupling itself is then achieved by defining a mixed-dimensional action functional with consistent Sobolev trace operators. Finally, we present numerical examples involving a three-dimensional silicone-rubber block reinforced with a curved graphite shell on its lower surface, a three-dimensional silver block reinforced with a graphite plate and beams, and lastly, intersecting silver shells reinforced with graphite beams. • The linear Cosserat micropolar model and its limit case for homogeneous Cauchy materia. • Derivations of Cosserat shell and beam models using tangential differential calculus. • A mixed-dimensional action functional via Sobolev trace operators for model-coupling. • Examination of the corresponding finite element spaces on codimensional domains. • Numerical examples to validate the approach and demonstrate its flexibility. [ABSTRACT FROM AUTHOR]
ISSN:00457825
DOI:10.1016/j.cma.2024.117384