Large deformation near a crack tip in a fiber-reinforced neo-Hookean sheet with discrete and continuous distributions of fiber orientations. (August 2021)

• Record Type: Journal Article
• Authors: Di Stasio, Luca; Liu, Yin; Moran, Brian
• Is Part Of: Theoretical and applied fracture mechanics. Volume 114(2021)
• Publication Date: 2021-08
• Subjects: Finite elasticity -- Neo-Hookean -- Fiber orientation distribution -- Crack tip fields -- Asymptotic analysis -- Finite element analysis (FEA); Fracture mechanics -- Periodicals; 620.1126
• DOI: 10.1016/j.tafmec.2021.103020
• Languages: English
• ISSNs: 0167-8442

Abstract

Highlights: The crack tip behavior of Neo-Hookean fiber-reinforced composite sheets is analyzed. Asymptotic isotropy is discovered for specific fiber orientation distributions. Asymptotic universal one-to-one anisotropic-to-isotropic mapping is found. Abstract: We consider crack tip deformations under plane stress conditions of a Neo-Hookean sheet reinforced by Neo-Hookean fibers, whose orientation and elastic properties are described by discrete and continuous spatial distributions. The mechanical behavior of the composite is described in terms of the first and fourth invariant of the right Cauchy-Green tensor following Guo et al. [1–3] . The crack tip integrals developed in Liu and Moran [4, 5] are used to determine the coefficients of the crack tip asymptotic expansion. The von Mises distribution of orientation is analyzed. The existence of a regime of isotropic behavior, which we call asymptotic isotropy, in the region of dominance of the asymptotic fields is established for certain combinations of fiber orientations. Finally, the possibility to construct an asymptotic universal one-to-one mapping between anisotropic and isotropic Neo-Hookean plane stress response at the crack tip is discussed.