Role of Fiber Orientations in the Mechanics of Bioinspired Fiber-Reinforced Elastomers

Abstract

Fiber reinforcement is a crucial attribute of soft bodied muscular hydrostats that have the ability to undergo large deformations and maintain their posture. Helically wound fibers around the cylindrical worm body help control the tube diameter and length. Geometric considerations show that a fiber winding angle of 54.7°, called the magic angle, results in a maximum enclosed volume. Few studies have explored the effects of differential fiber winding on the large deformation mechanics of fiber reinforced elastomers (FRE). We fabricated FRE materials in transversely isotropic layouts varying from 0-90° using a custom filament winding technique and characterized the nonlinear stress-strain relationships using uniaxial and equibiaxial experiments. We used these data within a continuum mechanical framework to propose a novel constitutive model for incompressible FRE materials with embedded extensible fibers. The model includes individual contributions from the matrix and fibers in addition to coupled terms in strain invariants, I1 and I4. The deviatoric stress components show inversion at fiber orientation angles near the magic angle in the FRE composites. These results are useful in soft robotic applications and in the biomechanics of fiber reinforced tissues such as the myocardium, arteries and skin.

On an Angle with Magical Properties

“…The magic angle is the optimal winding angle for the design of filament-wound structures and is often derived in the composites structures literature by what is known as "netting analysis." Further results with applications to soft robots are described in [15]. It was pointed out in [7] that the synthetic fibers in fire hoses are aligned at the magic angle to minimize sudden jerk as the hose is suddenly turned on.…”

A Bioinspired Fluid-Filled Soft Linear Actuator

“…Furthermore, a similar operation can be found in fiber-reinforced design 24 where the braided sleeve was used to constrain the deformation in the radial direction of the inflated chambers, 25 , 26 improve the stretch performance, 27 and facilitate the manufacturing. 28 …”

Elastomeric tubes with self-regulated distension

“…Under uniaxial tension, the same “J-shaped” stress-strain curve seen in aorta and many other biological tissues is also observed. Preferential or prescribed orientation of the fibers leads to the creation of anisotropic materials, which display resistance to certain deformation modes ( O’Connor, 1977 ; Beter et al., 2020 ; Chatterjee et al., 2021 ).…”