Hyperelastic Tube Research Articles (Page 1)

Replies to the comments by R. C. Batra on “Inflation, extension and torsion analysis of compressible functionally graded hyperelastic tubes” by M. Hajhashemkhani and M. R. Hematiyan, Acta Mech 231, 3947–3960 (2020)

Herniation, rotation, looping, and retraction of the midgut occur sequentially during midgut morphogenesis. Recent studies have demonstrated the importance of mechanical forces arising from the differential growth between the midgut and mesentery in the formation of small intestinal loops. However, the roles of mechanics and differential growth in the overall process remain unclear. In this study, we developed a computational model of midgut morphogenesis based on continuum mechanics. We showed that the protrusion, rotation, and retraction of the midgut can emerge sequentially because of temporal changes in differential growth. The midgut was modeled as a hyperelastic tube with a Gaussian shape. The differential growth of the midgut and mesentery was modeled by the spatial variation in spontaneous plastic deformation. The hyperelastic tube developed a protrusion by compression-induced deformation, suggesting that other external forces are not necessary for midgut herniation prior to rotation. Appropriate differential growth induced a rotation of the tube. A less-growing mesentery attempts to face inward to minimize the tensile forces, which causes tube twisting and results in midgut rotation. Excess differential growth may cause the retraction of the midgut before the formation of small intestinal loops. The results of this study will serve as reference in future studies on embryology and tissue engineering.

Pediatric intussusception is frequently observed in the ileocecal region, where the terminal ileum invaginates into the colon. Previous studies have indicated an association between pediatric intussusception and inflammation as well as intestinal motility. However, the underlying mechanisms remain unclear, particularly with regard to the mechanics. We hypothesized that invagination occurs when longitudinal and circular smooth muscles are not coordinated during peristalsis. To test the hypothesis from a mechanical perspective, we developed a computational model of the terminal ileum, where the terminal ileum is modeled as a hyperelastic tube. We showed that circumferential contraction with longitudinal relaxation of the hyperelastic tube wall caused invagination in the contracting region of the tube. We also found that invagination occurred when a square-shaped contracting region emerged in the hyperelastic tube. These results indicate that uncoordinated motion of the circular and longitudinal muscles can lead to invagination of the intestinal wall. In addition, the configuration of peristalsis may serve as an indicator of the risk of pediatric intussusception.

Comments on “Inflation, extension and torsion analysis of compressible functionally graded hyperelastic tubes” by Maedeh Hajhashemkhani and Mohammad Rahim Hematiyan, Acta Mech 231, 3947–3960 (2020)

Accurate and robust numerical simulation of hemodynamics is of interest for the identification and investigation of important physical or physiological quantities and their relationships to various cardiac and vascular functions. Comprehensive analysis requires efficiently simulating pressure and flow waves that travel and reflect through a complex network of vessels with varying geometric/material properties. This work introduces a new numerical methodology for modeling such wave propagation throughout the (closed-loop) circulation, employing a fast high-order (pseudo)spectral approach for resolving the well-established reduced-order one-dimensional Navier–Stokes hemodynamics formulations (coupled to hyperelastic tube laws) that govern the corresponding fluid–structure dynamics in each vascular segment. The model includes both systemic and pulmonary circulations and four heart chambers and four heart valves. Together with a correspondingly high-order treatment of multiscale zero-dimensional boundary conditions based on time-dependent ordinary differential equations, the overall solver has a number of attractive qualities: high-order accuracy in time and space; fast Fourier transform (FFT)-level computational efficiency; little to no numerical pollution errors (faithfully preserving the diffusion and dispersion characteristics of the underlying continuous operators); relatively mild Courant–Friedrichs–Lewy constraints for explicit temporal integration methods; robustness to extreme physiological parameters; and stable incorporation of the nonlinear and nonstationary coupling to other cardiovascular system components (e.g., heart chambers, valves, and microvasculature). The convergence properties, computational performance, and physiological accuracy of the proposed framework are demonstrated through a variety of numerical experiments that include applications to community benchmark problems previously proposed for mutual validation with other solvers (and three-dimensional or in vitro reference solutions).

Abstract This study introduces an analytical model for analyzing thermomechanical stresses in finite-length hyperelastic hollow cylinders under axial-torsional loading and non-isothermal conditions. The model incorporates an axial temperature distribution and decomposes strain responses into thermal expansion and mechanical stretches. Governing equations are derived using large deformation kinematics and the Neo-Hookean strain energy function. Solutions for displacements, stresses, and pressure variables are obtained with appropriate boundary conditions. Validation against 3D finite element analysis demonstrates strong agreement with significant computational cost savings. These findings challenge the conventional linear assumption for twist angles under large deformations. Increasing temperature differences introduce noticeable nonlinearities in radial and axial stress distributions, resulting in significant nonlinear axial stress distributions along the vertical walls. Additionally, higher temperature differences reduce axial stress at the inner radius, while shear stresses predominantly remain radial with minimal variation. In summary, this efficient analytical tool provides invaluable insights into thermomechanical stresses in soft active cylindrical components, with broad potential applications across various fields.

An enhanced version of the Rubber Cord Adhesion Inflation Test (RCAIT) has been designed to experimentally assess the internal pressure and cable tension applied to the specimen needed to propagate a crack along the matrix/reinforcement interface. To calculate the critical strain energy release rate, we develop a semi-analytical model describing the deformation of a hyperelastic tube under loading conditions that reflect the ones applied experimentally. A more comprehensive numerical model of the test is also proposed to investigate the influence of loading conditions on rubber deformation near the crack tip. Comparison of different experimental data sets with the theoretical/numerical data demonstrates that the new experimental setup allows for a reliable determination of the rubber/cord interface failure envelope under combined loading conditions.

Discussion of the paper “M. Askari-sedeh and M. Baghani, On the extension-torsion of short hyperelastic tubes of axially functionally-graded materials” [Eng Struct 301 (2024) 117344]

On the Extension-Torsion of Short Hyperelastic Tubes of Axially Functionally-Graded Materials

When a soft tube is inflated, it may sometimes show a bulge instability wherein a portion of the tube inflates much more than the rest. The bulge instability is well-understood for hyperelastic materials. We examine inflation of polyurethane tubes whose material behavior is not strictly hyperelastic. Upon inflating at constant rate, the tubes deform into a variety of shapes including irregular axisymmetric shapes with multiple localized bulges, a single axially-propagating bulge, or homogeneous cylindrical shapes. In all cases regardless of the inflation mode, the pressure first rises to a maximum, and then gradually reduces towards a plateau. We document numerous differences as compared to hyperelastic tubes. Most notably a pressure maximum can appear even without bulging, whereas for hyperelastic tubes, a pressure maximum is necessarily accompanied by bulging. Further, the decrease in pressure beyond the maximum occurs gradually over timescales as long as an hour, whereas bulging of hyperelastic tubes induces an instantaneous drop in pressure. We also observe permanent deformation upon deflation, a decrease in the pressure maximum during a subsequent second inflation, and more severe bulge localization at low inflation rates. Existing theory of hyperelastic tube inflation cannot capture the observed behaviors, even qualitatively. Finite element simulations suggest that many of the observations can be explained by viscoelasticity, specifically that a slow material response allows the pressure to remain high for long durations, which in turn allows growth of multiple bulges.

Ultimate equilibrium of a rigid cone enclosed in a hyperelastic membrane

A catalog of pressure and deformation profile for thin walled hyperelastic tubes conveying inertialess flow and undergoing large deformation

Twisting tubes as soft robotic valves

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Abstract Simple fiber reinforcing patterns can serve to guide deformations in specialized ways if the material experiences expansion due to some sort of swelling phenomenon. This occurs even when the only activation is via the material swelling itself; the fibers being a passive hyperelastic material embedded in a swellable hyperelastic matrix. Using anisotropic hyperelasticity where the usual incompressibility constraint is generalized to model swelling, we consider such fiber guided deformation in the context of a circular cylinder subject to uniform swelling. The material is taken to be transversely isotropic with a fiber pattern corresponding to helical spirals in each cross section. This paper extends previous work which had examined a traction free outer radius that expanded while the inner radius was held fixed. Because of the spiral pattern, the tube in these previous studies exhibited increasing twist as the swelling proceeded. The problem considered here takes both inner and outer radius as free surfaces, thus causing the amount of radial expansion itself to be unknown. It is found that the spiral fiber pattern again induces a twist, and that this pattern also influences the nature of the radial expansion.

While the buckling of tubes under axial compression has been extensively studied, the postbuckling behavior of thick tubes remains elusive. In this paper, we conduct three-dimensional buckling and postbuckling analysis for thick hyperelastic tubes subjected to axial compression under finite deformation by the asymptotic expansion method. Our theoretical results successfully predict the deformation and stress-strain curves of buckled tubes near the critical loading, which are well validated by finite element analysis. Depending on the geometry, three kinds of postbuckling paths, including continuous buckling, snap-through and snap-back, are discovered. We summarize our results in two phase diagrams of the critical stretch for the onset of buckling and postbuckling paths with respect to the geometric parameters. In particular, we have observed that the postbuckling response can undergo a complex transition among different types of postbuckling paths, including continuous buckling, snap-through and snap-back, which is attributed to the competition between two modes of deformation, i.e., global deformation and local distortion. When a tube is long and thick, it prefers global deformation, and its cross section remains almost a plane after buckling, whereas when a tube is relatively short and relatively thin, it prefers local distortion and its cross section does not remain a plane any more after buckling. Our work provides understanding and insights into the buckling and postbuckling of thick tubes, and bridges the knowledge gap between postbuckling of thick columns and tubes.

Effect of torsion on the initiation of localized bulging in a hyperelastic tube of arbitrary thickness

We provide an analytic derivation of the bifurcation conditions for localized bulging in an inflated hyperelastic tube of arbitrary wall thickness and axisymmetric necking in a hyperelastic sheet under equibiaxial stretching. It has previously been shown numerically that the bifurcation condition for the former problem is equivalent to the vanishing of the Jacobian determinant of the internal pressure P and resultant axial force N, with each of them viewed as a function of the azimuthal stretch on the inner surface and the axial stretch. This equivalence is established here analytically. For the latter problem for which it has recently been shown that the bifurcation condition is not given by a Jacobian determinant equal to zero, we explain why this is the case and provide an alternative interpretation.

On propagation of waves in pressurized fiber-reinforced hyperelastic tubes based on a reduced model

Mechanical instability in a pre-tensioned finite hyperelastic tube subjected to a slowly increasing internal pressure produces a spatially localized bulge at a critical pressure. This instability is studied in controlled experiments on inflated latex rubber tubes, from the perspective of buckling observed in aneurysms and their rupture risk. The fate of the bulge under continued inflation is governed by the end-conditions and the initial tension in the tube. In a tube with one end fixed and a weight attached to the other freely moving end, the bulge propagates axially at low initial tension, growing in length, and the tube relaxes by extension without buckling. Rupture occurs when the tension is high. By contrast, the bulge formed in an initially stretched tube held fixed at both its ends can buckle or rupture, depending on the amount of initial tension. Experiments are reported for different initial tensions and boundary conditions (BCs). Failure maps in the stretch parameter space and in stretch–tension space are constructed by extending existing theories for bulge formation and buckling analyses to the experimentally relevant BCs. Failure maps deduced from the theory are compared against experiments, and the underlying assumptions are critically assessed. Experiments reveal that buckling provides an alternative route to relieve the stress built up during inflation. Hence, buckling, when it occurs, can be a protective fail-safe mechanism against the rupture of a bulge in an inflated elastic tube.