A semi-empirical approach model for neo-Hookean solids

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 th...

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Bibliographic Details
Published in:International journal of computational methods in engineering science and mechanics Vol. 24; no. 2; pp. 155 - 166
Main Author: Abdel-Rahman, A. S.
Format: Journal Article
Language:English
Published: Taylor & Francis 04.03.2023
Subjects:
critical elongation
internal friction
Mooney-Rivlin
neo-Hookean
stress-strain
ISSN:1550-2287, 1550-2295
Online Access:Get full text
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Summary: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.
ISSN:1550-2287
1550-2295
DOI:10.1080/15502287.2022.2113184