Search
Abstract
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.
Citations
-
3
CrossRef
-
0
Web of Science
-
2
Scopus
Authors (4)
-
Thang X. Duong dr
-
Vu N Khiêm
-
Mikhail Itskov
Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1177/10812865221104427
- License
-
open in new tab
Keywords
Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
MATHEMATICS AND MECHANICS OF SOLIDS
no. 28,
pages 1274 - 1317,
ISSN: 1081-2865 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- 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:
- Digital Object Identifier (open in new tab) 10.1177/10812865221104427
- Sources of funding:
-
- Free publication
- Verified by:
- Gdańsk University of Technology
seen 103 times