Predictions of aneurysm formation in distensible tubes: Part B—Application and comparison of alternative approaches

Abstract

The theoretical treatise of the companion paper produced three distinct approaches of increasing complexity. Just as the presented theory is equally applicable to other medical, scientific or engineering applications, so the systematic numerical investigation now reported is relevant to these fields of study. An independently developed finite element analysis (FEA) solution is used to show that the commercial package selected provides critical pressure predictions of a consistent order of magnitude. The FEA sensitivity analysis considers five distinct elements with up to seven alternative strain-energy functions and different combinations of uniaxial, equi-biaxial and pure shear data sets to identify the effect on critical pressure prediction and overall behaviour of a pressurised distensible tube. This represents the most comprehensive comparative study available in the open literature. For a selected strain-energy function the impact of the variation of length to initial radius and wall thickness to initial radius are investigated. Thereafter it is demonstrated that these two ratios rather than actual dimensions are the driving factors behind pressurised tube behaviour.

The role of constitutive relation in the stability of hyper-elastic spherical membranes subjected to dynamic inflation

“…This highlights how crucial may be the selection of the (appropriate) strain-energy function for (reliable) mathematical modelling of hyper-elastic membranes subjected to dynamic solicitations. As such, our investigation complements recent papers developed under similar premises but within the static regime, see (Biscari & Omati, 2010;Bucchi & Hearn, 2013a, 2013bMangan & Destrade, 2015).…”

“…The material parameters of the strain-energy functions are taken from Hearn (2013a, 2013b), where the same set of experimental results (Treolar, 1944) was used to calibrate the models. Further, the same fitting procedure was followed to identify the material parameters of all the strain-energy functions considered (Bucchi & Hearn, 2013a, 2013b. It can be easily checked that, despite they are not identical, the predictions of these 6 constitutive models within the linear limit are rather similar.…”

“…Moreover C Mk ij are material constants. Three different models of the Mooney-Rivlin family (Rivlin, 1948;Treolar, 1944Treolar, , 1949Yeoh, 1993), frequently used to approximate the constitutive behaviour of elastomeric solids (Beatty, 2009;Bucchi & Hearn, 2013a, 2013bVolokh & Vorp, 2008;Wolters et al, 2005), are considered:…”

“…Three different models of the Ogden family (Ogden, 1972(Ogden, , 1997, frequently used to approximate the constitutive behaviour of elastomeric solids (Bucchi & Hearn, 2013a, 2013bDestrade, Annaidh, & Ciprian, 2009;Fu & Xie, 2012;Volokh, 2011), are considered:…”

“…It is pointed out by Bucchi and Hearn (2013b) that, in the recent literature, too often only one strain-energy function is used to describe the material behaviour. Even if two or more strain-energy functions are utilised, their parameters are frequently taken from different sources.…”