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A general theory for anisotropic Kirchhoff–Love shells with in-plane bending of embedded fibers

Abstrakt

This work presents a generalized Kirchhoff–Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for heterogeneous and fibrous materials such as textiles, biomaterials, composites and pantographic structures. The presented theory is a direct extension of classical Kirchhoff–Love shell theory to incorporate the in-plane bending resistance of fibers. It also extends existing second-gradient Kirchhoff–Love shell theory for initially straight fibers to initially curved fibers. To describe the additional kinematics of multiple fiber families, a so-called in-plane curvature tensor—which is symmetric and of second order—is proposed. The effective stress tensor and the in-plane and out-of-plane moment tensors are then identified from the mechanical power balance. These tensors are all second order and symmetric in general. Constitutive equations for hyperelastic materials are derived from different expressions of the mechanical power balance. The weak form is also presented as it is required for computational shell formulations based on rotation-free finite element discretizations. The proposed theory is illustrated by several analytical examples.

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Wersja publikacji
Accepted albo Published Version
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1177/10812865221104427
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Creative Commons: CC-BY-NC otwiera się w nowej karcie

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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuły w czasopismach
Opublikowano w:
MATHEMATICS AND MECHANICS OF SOLIDS nr 28, strony 1274 - 1317,
ISSN: 1081-2865
Język:
angielski
Rok wydania:
2022
Opis bibliograficzny:
Duong T. X., Khiêm V. N., Itskov M., Sauer R.: A general theory for anisotropic Kirchhoff–Love shells with in-plane bending of embedded fibers// MATHEMATICS AND MECHANICS OF SOLIDS -Vol. 28,iss. 5 (2022), s.1274-1317
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1177/10812865221104427
Źródła finansowania:
  • COST_FREE
Weryfikacja:
Politechnika Gdańska

wyświetlono 47 razy

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