Gent models for the inflation of spherical balloons

TL;DR

This paper compares different phenomenological models for rubber balloon inflation, finding that the Gent-Gent (GG) model best captures the experimental data and underlying physics.

Contribution

It evaluates and compares the Mooney and Gent-Gent models for balloon inflation, establishing the GG model as the most accurate and versatile.

Findings

GG model provides the best fit to experimental data

Basic physics exclude certain models like Varga and Ogden

Link established between elasticity solutions and membrane theories

Abstract

We revisit an iconic deformation of non-linear elasticity: the inflation of a rubber spherical thin shell. We use the 3-parameter Mooney and Gent-Gent (GG) phenomenological models to explain the stretch-strain curve of a typical inflation, as these two models cover a wide spectrum of known models for rubber, including the Varga, Mooney-Rivlin, one-term Ogden, Gent-Thomas and Gent models. We find that the basic physics of inflation exclude the Varga, one-term Ogden and Gent-Thomas models. We find the link between the exact solution of non-linear elasticity and the membrane and Young-Laplace theories often used a priori in the literature. We compare the performance of both models on fitting the data for experiments on rubber balloons and animal bladder. We conclude that the GG model is the most accurate and versatile model on offer for the modelling of rubber balloon inflation.