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Calculation of the strength of spirally organized cellulose fibers using the generalized Euler-Eitelwein formula

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Abstract

A theoretical model has been proposed to investigate the strength of helical coupling of nanocellulose into nanofibrils and nanofibrils into microfibrils. Namely, the force held by an elastic rod uniformly wrapped around a cylinder in a helix with a finite step was calculated. The initial shape of the elastic rod in the unstressed state was assumed to be helical (rather than rectilinear). The bending stiffness of the rod was taken into account. We have also taken into account the Coulomb friction and adhesion of the rod to the cylinder, which prevents slippage, and their attraction, which prevents detachment. Our result generalizes the Euler–Eitelwein formula for winding a thread normal to the generatrix of a rough cylinder in the absence of thread bending stiffness and attraction to the cylinder. We found that the spatial nature of the winding significantly reduces the strength of the helical connection, but it is still much stronger than a non-helical connection.

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  1. N.N. Semenov Federal Research Center for Chemical Physics of Russian Academy of Science, Moscow, Russian Federation

    Aleksey Skoblin, Maria Mikhaleva & Sergey Stovbun

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  1. Aleksey Skoblin
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  2. Maria Mikhaleva
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  3. Sergey Stovbun
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Correspondence to Aleksey Skoblin.

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Skoblin, A., Mikhaleva, M. & Stovbun, S. Calculation of the strength of spirally organized cellulose fibers using the generalized Euler-Eitelwein formula. Meccanica 57, 1631–1637 (2022). https://doi.org/10.1007/s11012-022-01520-w

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