Predictions of aneurysm formation in distensible tubes: Part A—Theoretical background to alternative approaches

Abstract

Pressurised distensible tubes are subject to aneurysms. Aneurysm inception will take place at a location along the tube when a critical pressure, relative to tube wall thickness at that location, is reached. Parents will recognise the existence of critical pressure when endeavouring to inflate a party balloon. Another example of aneurysm is the thoracic aortic aneurysm corresponding to permanent dilation of the aorta in such proportions that it can be life threatening. Corrective procedures for aortic aneurysms involve the introduction of stiff materials to prevent aneurysm. Similarly in a proposed distensible tube based wave energy device aneurysm inception is partially controlled through the use of alternative longitudinal strips of inextensible material and appropriate rubber strips. Here we consider distensible tubes made of one material.Having reviewed the aneurysm based literature some inconsistencies were observed between the material properties used in a non-linear finite element analysis and the material properties of the specimen used to provide experimental measurements for comparison. To appreciate the inconsistencies the authors decided to investigate aneurysm development using both non-linear finite element analyses and distinct alternative formulations and solution techniques. Rather than restrict strain-energy function to a subset of Neo-Hookean, Mooney–Rivlin and Ogden forms, the authors have implemented several alternative strain-energy models in parallel, also exploring for the first time the impact of using different combinations of uniaxial, equi-biaxial and pure shear experimental data for different rubbers.This paper addresses the needs (necessary considerations, such as the Valanis–Landel hypothesis, Maxwell equal area rule and data selection criteria) for a realistic approach to modelling a distensible tube to provide predictions of critical pressure. In common with all other cited references a static analysis is used.