Bulging bifurcation of inflated circular cylinders of doubly fiber-reinforced hyperelastic material under axial loading and swelling

Abstract

In this paper, we examine the influence of swelling on the bulging bifurcation of inflated thin-walled cylinders under axial loading. We provide the bifurcation criteria for a membrane cylinder subjected to combined axial loading, internal pressure and swelling. We focus here on orthotropic materials with two preferred directions which are mechanically equivalent and are symmetrically disposed. Arterial wall tissue is modeled with this class of constitutive equation and the onset of bulging is considered to give aneurysm formation. It is shown that swelling may lead to compressive hoop stresses near the inner radius of the tube, which could have a potential benefit for preventing aneurysm formation. The effects of the axial stretch, the strength of the fiber reinforcement and the fiber winding angle on the onset of bifurcation are investigated. Finally, a boundary value problem is studied to show the robustness of the results.

Localized bulging in an inflated cylindrical tube of arbitrary thickness – the effect of bending stiffness

“…It is therefore a fundamental protypical problem whose understanding can help shed light on other more complicated localization problems. The problem itself is relevant to a variety of applications, as witnessed by a series of recent studies on the continuum-mechanical modelling of aneurysm initiation in human arteries Alhayani et al, 2013Alhayani et al, , 2014Rodrguez-Martnez et al, 2015), and on localized bulging under the additional effects of swelling (Demirkoparan & Merodio, 2015), viscoelasticity/chemorheology (Wineman, 2015a,b), and electric actuation (Lu et al, 2015).…”

Line and point defects in nonlinear anisotropic solids

“…that models the coupling between the fibers (in N 1 and N 2 directions) is needed to express the energy function for monoclinic materials as N 1 and N 2 are not perpendicular (see [39,58,7]). Therefore…”

Effect of double-fibre reinforcement on localized bulging of an inflated cylindrical tube of arbitrary thickness

“…As demonstrated in our earlier papers, see, e.g., Fu et al [5], a most transparent way to understand the initiation of localized bulging is by plotting the solution of the bifurcation condition Ω(λ a , λ z ) = 0 and the equation F(λ a , λ z ) = F 0 together in the (λ a , λ z )-plane, where F 0 is a constant. This is achieved numerically in a straightforward manner with the aid of Mathematica [18]. The curve F(λ a , λ z ) = F 0 is of course only relevant when the resultant axial force is fixed to be equal to F 0 , in which case the curve represents the appropriate loading path in the (λ a , λ z )-plane.…”