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

• Published in: Theoretical and applied fracture mechanics 2021-08, Vol.114, p.103020, Article 103020
• Main Authors: Di Stasio, Luca, Liu, Yin, Moran, Brian
• Format: Article
• Language: English
• Subjects: Asymptotic analysis; Asymptotic properties; Asymptotic series; Crack tip fields; Crack tips; Deformation; Elastic properties; Fiber orientation; Fiber orientation distribution; Fiber reinforced materials; Finite elasticity; Finite element analysis (FEA); Isotropy; Mechanical properties; Neo-Hookean; Plane stress; Spatial distribution; Tensors
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/j.tafmec.2021.103020

•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. 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.