Swelling of an internally pressurized nonlinearly elastic tube with fiber reinforcing

Abstract

We study the effect of swelling on the mechanical response of fiber reinforced tubes within the context of finite elastic deformation. The fibers themselves do not swell, setting up a competition between the matrix, for which swelling tends to open the tube, and the fibers, for which swelling tends to constrict the tube. Balancing these tendencies in the constitutive response can lead to an internal channel opening that remains relatively constant over a wide range of swelling. Further, the hoop stress on the inner wall in such a situation may be compressive, rather than tensile. Both effects may be advantageous in certain settings, including biological organ systems.

Computational modelling suggests good, bad and ugly roles of glycosaminoglycans in arterial wall mechanics and mechanobiology

“…We used both a mixture-based finite-element model [27] to examine gross mechanical consequences of transmural differences in GAG-associated FCD in the arterial wall and a semi-analytical continuum model [29] to examine phenomenologically the biomechanical consequences of the resulting transmural differences in intralamellar swelling. Consistent with general findings on the equivalence of short-term soft tissue responses modelled using a biphasic mixture theory and an incompressible finite elasticity theory [48], we also found that predicted gross mechanical metrics were very similar using these two approaches (table 3 and figure 4).…”

“…Although swelling causes a change in volume, the swollen artery appears to deform isochorically thereafter in response to transient loading; hence, one can use incompressible finite elasticity provided the swelling is included. Towards this end, we used but extended the method of Demirkoparan & Pence [29], who analysed effects of swelling on fibre-reinforced cylindrical tubes with v à ¼ detF a constant function of radius. We first studied the effect of a constant swelling on a bilayered arterial model, but then studied effects of more physiological situations wherein the media swelled more than the adventitia.…”

Hyperelastic modeling of swelling in fibrous soft tissue with application to tracheal angioedema

“…When the effect of mechanical stress on tissue volume is relatively modest, then the material is barely compressible. The zero compressibility limit of such a description then generates the type of hyperelastic swelling theory studied in Tsai et al (2004) for the isotropic case and in Demirkoparan and Pence (2007) for the fiber reinforced case.…”

Torsional Swelling of a Hyperelastic Tube with Helically Wound Reinforcement

“…The general framework, in which swelling is described in terms of the prescribed field v * , is the same as that employed in [1,2]. These earlier papers only considered purely radial deformations due to swelling in fiber reinforced hyperelastic materials.…”

“…Torsion was not considered in this previous work because attention was there restricted to an azimuthally balanced fiber reinforcement associated with two counterpoised fiber families. The constitutive theory employed both here and in [1,2] is presented in Section 2. It presumes that the material is incompressible after swelling so that the determinant of the deformation gradient is everywhere equal to the value of the swelling field.…”