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Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes [article]

Ivo Steinbrecher, Alexander Popp, Christoph Meier
2021 arXiv   pre-print
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]

Alexander Popp, Ivo Steinbrecher
2021 arXiv   pre-print
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]

Sanjay Dharmavaram, Hossein Ebrahimi, Ranajay Ghosh
2021 arXiv   pre-print
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]

Tomohiko G. Sano, Matteo Pezzulla, Pedro M. Reis
2021 arXiv   pre-print
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]

Maximilian J. Grill, Wolfgang A. Wall, Christoph Meier
2019 arXiv   pre-print
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

Maximilian J. Grill, Wolfgang A. Wall, Christoph Meier
2020 International Journal for Numerical Methods in Engineering  
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

M. Ostoja-Starzewski, J. Li, H. Joumaa, P.N. Demmie
2013 Zeitschrift für angewandte Mathematik und Mechanik  
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

D. Polyzos, D.I. Fotiadis
2012 International Journal of Solids and Structures  
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]

Ustim Khristenko, Stefan Schuß, Melanie Krüger, Felix Schmidt, Barbara Wohlmuth, Christian Hesch
2021 arXiv   pre-print
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

D LIU
2004 Journal of the mechanics and physics of solids  
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

D LIU
2004 Journal of the mechanics and physics of solids  
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

A. Klar, N. Marheineke, R. Wegener
2009 Zeitschrift für angewandte Mathematik und Mechanik  
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

Anik Kumar Ghosh, Swagato Sarkar, Lisa Julia Nebel, Olha Aftenieva, Vaibhav Gupta, Oliver Sander, Amit Das, Joby Joseph, Sven Wießner, Tobias A. F. König, Andreas Fery
2021 Advanced Functional Materials  
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

Chenghao Yang, Rongjie Kang, David T. Branson, Lisha Chen, Jian S. Dai
2019 Mechanism and Machine Theory  
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

Giovanni Garcea, Antonio Madeo, Raffaele Casciaro
2012 Journal of Mechanics of Materials and Structures  
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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