Exponents of the one-term Ogden model: insights from simple shear. (17th October 2022)

• Record Type: Journal Article
• Authors: Horgan, Cornelius O.; Murphy, Jeremiah G.
• Is Part Of: Philosophical transactions. Volume 380:Number 2234(2022)
• Publication Date: 2022-10-17
• Subjects: incompressibility -- nonlinear elasticity -- Ogden invariants -- simple shear; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2021.0328
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : Isotropic one-term Ogden models are widely used to predict the mechanical response of both incompressible elastomers and soft tissue. Even though the exponent might be chosen to yield excellent agreement with some aspects of mechanical response, there is no guarantee that these models will be physically realistic in all situations. We show here that, in particular, the predictions of models with either negative or large positive exponents do not seem physically realistic in simple shear. The mechanical response of materials in shear should be physically realistic to ensure rational and reliable predictions for complex geometries and boundary conditions. We suggest that for problematic values of exponents of one-term models that extra Ogden invariants should necessarily be included in the model. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.