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Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes
[article]
2021
arXiv
pre-print
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This article proposes a mortar type finite element formulation for consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into 3D solid volumes. ...
A consistent 1D-3D coupling scheme for this problem type is proposed, which enforces both positional and rotational constraints. ...
Thus, the problem of beams embedded in a 3D solid volume can be classified as mixed-dimensional 1D-3D coupling problem between 1D Cosserat continua and a 3D Boltzmann continuum. ...
arXiv:2107.11151v1
fatcat:t32fdmfcjfg23jx2n2n23bxfpy
Finite Element Formulations for Beam-to-Solid Interaction – From Embedded Fibers Towards Contact
[article]
2021
arXiv
pre-print
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Therefore, this contribution gives an overview of current steps being taken, starting from state-of-the-art beam-to-beam (1D) and solid-to-solid (3D) contact algorithms, towards a truly general 1D-3D beam-to-solid ...
This is particularly true for the case of beam-to-solid interaction with its mixed-dimensional 1D-3D contact models. ...
In the following, an overview of the first steps taken in this direction is given, i.e. tied contact formulations for 1D fibers being embedded into 3D solid bodies [22] . ...
arXiv:2107.11158v1
fatcat:lv72odojjfcshhrxuiruu23zve
Coupled Bend-Twist Mechanics of Biomimetic Scale Substrate
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2108.10976v1 fatcat:jhh227l5dnfidoqmprsx4275ua
We develop the mechanics of combined bending and twisting deformation of a one-dimensional filamentous structure with protruding stiff fish-scale-like plates embedded at an angle on the surface. ...
The derived structure-property relationships reveal for the first time the combined effect of bending and twisting on a slender fish scale inspired substrate. ...
Acknowledgement This work was supported by the United States National Science Foundation's Civil, Mechanical, and Manufacturing Innovation, CAREER Award #1943886. ...
arXiv:2108.10976v2
fatcat:iwrfd2rpdrcmhlgwmt34ea2emu
A Kirchhoff-like theory for hard magnetic rods under geometrically nonlinear deformation in three dimensions
[article]
2021
arXiv
pre-print
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By reducing the 3D description into 1D or 2D via dimensional reduction, several theories of hard magnetic slender structures such as linear beams, elastica, and shells have been recently proposed. ...
Our theory is based on reducing the 3D magneto-elastic energy functional for the hard MREs into a 1D Kirchhoff-like description. ...
The magnetization density vector per unit volume in the deformed configuration is modeled as the "rotation" of B r as M 3D = FB r /µ 0 . ...
arXiv:2106.15189v1
fatcat:fmtretkbhzewdg7n47kt6h54ee
A Computational Model for Molecular Interactions Between Curved Slender Fibers Undergoing Large 3D Deformations With a Focus on Electrostatic, van der Waals and Repulsive Steric Forces
[article]
2019
arXiv
pre-print
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A direct evaluation of the total interaction potential for general 3D bodies requires the integration of contributions from molecule or charge distributions over the volumes of the interaction partners ...
This contribution proposes the first 3D beam-to-beam interaction model for molecular interactions between curved slender fibers undergoing large deformations. ...
This in turn allows for a reduced dimensional description as a 1D Cosserat continuum embedded in the 3D Euclidian space. ...
arXiv:1907.12997v2
fatcat:4pday6wll5bjzapaj4cu5qtu6a
A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces
2020
International Journal for Numerical Methods in Engineering
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By contrast, the beam theory describes a slender body as a one-dimensional (1D) Cosserat continuum, such that a further reduction in the dimensionality and thus computational cost can be achieved. ...
of surface interactions and a six-dimensional (6D) integral over both volumes for volume interactions, respectively. ...
This, in turn, allows for a reduced dimensional description as a 1D Cosserat continuum embedded in the 3D Euclidian space. ...
doi:10.1002/nme.6309
fatcat:tlpd46vjfba75nob47cvug3mca
From fractal media to continuum mechanics
2013
Zeitschrift für angewandte Mathematik und Mechanik
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Following an account of this method, we develop balance laws of fractal media (continuity, linear and angular momenta, energy, and second law) and discuss wave equations in several settings (1d and 3d ...
wave motions, fractal Timoshenko beam, and elastodynamics under finite strains). ...
Also, the support of the first author as Timoshenko Distinguished Visitor in the Division of Mechanics and Computation, Stanford University, is gratefully acknowledged. www.zamm-journal.org ...
doi:10.1002/zamm.201200164
fatcat:7fpfsqoaf5ak3d4yigqljnjusm
Derivation of Mindlin's first and second strain gradient elastic theory via simple lattice and continuum models
2012
International Journal of Solids and Structures
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The first is based on the standard continualization of the equation of motion taken for a sequence of mass-spring lattices, while the second one exploits average processes valid in continuum mechanics. ...
Solids Struct. 1, 417-438, 1965, proposed two enhanced strain gradient elastic theories to describe linear elastic behavior of isotropic materials with micro-structural effects. ...
Acknowledgements The first author is grateful to IKYDA2010 program for supporting this work. ...
doi:10.1016/j.ijsolstr.2011.10.021
fatcat:rb55lk626zaqtp3pcjvfy7kl5e
Multidimensional coupling: A variationally consistent approach to fiber-reinforced materials
[article]
2021
arXiv
pre-print
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The coupling conditions acknowledge both, the forces and the moments of the beam model and transfer them to the background material. ...
It is based on a 1-dimensional beam model for the thin fiber structures, a flexible and general 3-dimensional elasticity model for the matrix and an overlapping domain decomposition approach. ...
Acknowledgements We would like to thank the group of Alexander Popp at the Universität der Bundeswehr München and his Co-Worker Ivo Steinbrecher for providing us additional data for the benchmark test. ...
arXiv:2101.02527v3
fatcat:lhnawfbm6bexvg75jubacgt2gu
Compressive strength of fibre composites with random fibre waviness
2004
Journal of the mechanics and physics of solids
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An ensemble of ÿbre waviness proÿles is generated from an assumed spectral density of waviness and the compressive strength for each such realisation is calculated directly by the ÿnite element method. ...
The e ect of the physical size of waviness is addressed by using couple stress theory, with the ÿbre bending resistance scaling with the ÿbre diameter d. ...
They assumed that the ÿbres behave as linear elastic beams embedded within a non-linear dilatant matrix. ...
doi:10.1016/s0022-5096(04)00011-0
fatcat:ijwib27j4zduxgdvfdpqskhdsy
Compressive strength of fibre composites with random fibre waviness
2004
Journal of the mechanics and physics of solids
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An ensemble of ÿbre waviness proÿles is generated from an assumed spectral density of waviness and the compressive strength for each such realisation is calculated directly by the ÿnite element method. ...
The e ect of the physical size of waviness is addressed by using couple stress theory, with the ÿbre bending resistance scaling with the ÿbre diameter d. ...
They assumed that the ÿbres behave as linear elastic beams embedded within a non-linear dilatant matrix. ...
doi:10.1016/j.jmps.2004.01.005
fatcat:bi3jkp7avbeunhvuovbt2nudse
Hierarchy of mathematical models for production processes of technical textiles
2009
Zeitschrift für angewandte Mathematik und Mechanik
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They are theoretically and numerically analyzed and coupled via asymptotic analysis, similarity estimates and parameter identification. ...
In this work we establish a hierarchy of mathematical models for the numerical simulation of the production process of technical textiles. ...
and software for fiber dynamics in the mentioned production processes, especially the used Fiber Dynamics Simulation Tool (FIDYST). ...
doi:10.1002/zamm.200900282
fatcat:hgoemqeawvh7xpts2ozdn6ee3y
Exploring Plasmonic Resonances Toward "Large‐Scale" Flexible Optical Sensors with Deformation Stability
2021
Advanced Functional Materials
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Subsequently, both continuous and discontinuous 1D-metallic lattices are obtained via vapor deposition of gold at different angles. ...
The LSPR supported flexible sensor provides superiority in terms of sensitivity, which is investigated under mechanical deformations to exhibit consistency of the resonant wavelength. ...
Open access funding enabled and organized by Projekt DEAL.
Conflict of Interest The authors declare no conflict of interest.
Data Availability Statement Research data are not shared. ...
doi:10.1002/adfm.202101959
fatcat:fwsw7h2xbvfi5abasjbykamctq
Kinematics and statics of eccentric soft bending actuators with external payloads
2019
Mechanism and Machine Theory
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Soft bending actuators, born with the considerable capacity of structural flexibility and environmental adaptability, have been widely favored for years. ...
Following this, the static model takes the input pressure, external payloads, and material parameters into account by utilizing the principle of minimum potential energy, making a generalized mathematical ...
Acknowledgment The financial support from the National Key R&D Program of China (Grant no. 2018YFB1304600), the Natural Science ...
doi:10.1016/j.mechmachtheory.2019.05.015
fatcat:yzb2oohsjnaerko2pl6lnpsqmu
The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates
2012
Journal of Mechanics of Materials and Structures
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What we call the implicit corotational method is proposed as a tool to obtain geometrically exact nonlinear models for structural elements, such as beams or shells, undergoing finite rotations and small ...
the embedded linear solution. ...
Acknowledgements Support from the Office of Naval Research through a Multidisciplinary University Research Initiative Program on "Cellular Materials Concepts for Force Protection," Prime Award No. ...
doi:10.2140/jomms.2012.7.509
fatcat:lqle7qihjzgf7eyddayxs3hiyu
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