The inflation of viscoelastic balloons and hollow viscera

Abstract

For the first time, the problem of the inflation of a nonlinear viscoelastic thick-walled spherical shell is considered. Specifically, the wall has quasilinear viscoelastic constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of murine bladders . While the associated nonlinear elastic problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent nonlinear viscoelastic case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is not independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the nonlinear Volterra integral equation in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure.

Likely oscillatory motions of stochastic hyperelastic solids

“…It was concluded that, as the amplitude and period of oscillations are strongly influenced by the rate of internal pressure, if the pressure was suddenly imposed and the inflation process was short, then sustained oscillations due to the dominant elastic effects could be observed. However, for many systems under slowly increasing pressure, strong damping would generally preclude oscillations [27]. More recently, the dynamic response of incompressible hyperelastic cylindrical and spherical shells subjected to periodic loading was discussed in [79,80].…”

Dynamic persistence of intracellular bacterial communities of uropathogenicEscherichia coliin a human bladder-chip model of urinary tract infections

“…Voiding of the bladder through urination rapidly reduces bladder volume, (‘ voiding bladder state’) and removes the strain experienced by the bladder cells. The bladder epithelium, as a viscoelastic material, responds to the removal of strain and relaxes over the subsequent period (Pascalis et al, 2018) where the bladder volume remains low (‘ voided bladder state’) (Fig. 1D).…”

A Recruitment Model of Tendon Viscoelasticity That Incorporates Fibril Creep and Explains Strain-Dependent Relaxation

“…¼ 0:17 (27) Therefore, to complete our relaxation function, we still need to independently determine one of the three relaxation moduli. We therefore used the literature on rat tail tendon fibril Young's moduli to determine the value of E 1 .…”

“…Experiments show that rates of relaxation and creep are dependent on the strain or stress level that is being imposed [22,23]. The latter rules out the possibility of employing quasilinear viscoelasticity (QLV) (which is based on the work of Fung [24] and has recently been reinterpreted by De Pascalis et al [25], extended to the case of transverse isotropy by Balbi et al [26] and employed for modeling viscoelastic inflation problems by De Pascalis et al [27]) with a single scalar relaxation function. QLV assumes that the viscous relaxation rate is independent of the instantaneous local strain and is a special case of the more general constitutive model developed by Pipkin and Rogers [28].…”