Analytical and numerical analysis of the mechanical behavior of spherical soft materials for a biomedical application: comparison of different models

Abstract

This paper aims to investigate the stress field of a hollow sphere with thick walls made of a homogenous, isotropic, nonlinearly hyperelastic solid under internal or external pressure. It investigates various loading scenarios: exclusive internal pressure, exclusive external pressure and the simultaneous application of both. An analytical solution is derived in the case of incompressible sphere utilizing strain energy density functions from Neo-Hookean, Mooney–Rivlin and Yeoh models and a compressible Neo-Hookean constitutive equation in the case of the compressible one. To validate this solution, a finite element model is developed for the pressurized spherical vessel. Comparison between the analytical non-dimensional stress components and finite element method results shows strong agreement, confirming the accuracy of both approaches. The analysis reveals that under external pressure alone or combined internal and external pressures, all three constitutive models predict similar stress values. However, under internal pressure without external pressure, the Yeoh model consistently forecasts higher stress values than the Neo-Hookean and Mooney–Rivlin models, indicating that the choice of constitutive model significantly influences stress predictions under specific loading conditions. Additionally, for compressible hyperelastic materials, results indicate that maximum dilation of the sphere decreases with increasing Poisson’s ratio.