A semi-empirical approach model for neo-Hookean solids

Abstract

The neo-Hookean materials change their behaviour at large stress values to give more strain than linear trend (Hook’s region) and plastic deformations appear and ultimately fail. A Mooney-Rivlin model successfully describes this behaviour based on theoretical derivations deduced from Kinetic theory. Although the model takes into account that the deformation involves a change in the volume of rubber, their relationship is quite fitting for a small stress-strain region (Gaussian region). In the present work, a peer model to Mooney-Rivlin one was presented, which covers the full behaviour of the stress-strain relationship. It is based on the theoretical derivation of the critical elongation value, which has been noticed previously in many earlier works but not theoretically defined. The internal friction coefficient, as a mechanical property of the material, was introduced in this model. Unexpectedly, the behaviour of elastic materials at small stress values is not Hookean but shows constant strain as the stress increases in a very small region.

HIGHLIGHTS

• The critical elongation value is theoretically driven.

• Internal friction, which is a mechanical property of the material, is presented as a variable in the stress-strain model.

• Showing the behaviour of elastic materials at small stress values.

• Extend the well-known Mooney-Rivlin model to cover the stress-strain regime.

Keywords:

• Mooney-Rivlin
• neo-Hookean
• stress-strain
• critical elongation
• internal friction

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.