Continuum models for pantographic blocks with second gradient energies which are incomplete

Stilz, Maximilian; Dell’Isola, Francesco; Giorgio, Ivan; Eremeyev, Victor A.; Ganzenmüller, Georg; Hiermaier, Stefan

doi:10.1016/j.mechrescom.2022.103988

Cited by 16 publications

(2 citation statements)

References 25 publications

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“…in terms of the metric of relative twists. The minimization problem (10) can efficiently be solved using trustregion methods or a Levenberg-Marquardt algorithm.…”

Section: Numerical Modelmentioning

confidence: 99%

“…Constraining the periodicity of the arrangement of beams to only one dimension, we can describe a pantographic beam [1][2][3][4] and for two dimensions a pantographic sheet [5][6][7][8]. By adding additional parallel pantographic sheets, which are all interconnected by pivots, pantographic blocks are formed, and a periodicity is added to the third dimension [9][10][11]. For pantographic ortho-blocks, the additional parallel sheets are interconnected by orthogonal pantographics sheets instead of pivots [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Chirality effects in panto-cylindrical structures

Stilz,

Breuling,

Eugster

et al. 2024

Mathematics and Mechanics of Solids

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In this paper, we apply a numerical integration strategy recently developed for determining the deformation shapes of structures constituted by Cosserat rods, to predict the behavior of panto-cylinders. Panto-cylinders have, as microstructure, a set of two families of helicoidal beams interconnected by perfect or elastic joints. The pivot’s free rotation axis is, in the reference configuration, orthogonal to the cylindrical surfaces spanned by the beams. We perform a series of numerical simulations looking for the mechanical parameters which exalt the chirality effects in the structure. For the performed compression, extensions, shear, and torsion tests, we find chiral deformation patterns with a dependence on the type of joint and its length.

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“…in terms of the metric of relative twists. The minimization problem (10) can efficiently be solved using trustregion methods or a Levenberg-Marquardt algorithm.…”

Section: Numerical Modelmentioning

confidence: 99%