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Polymers 2016, 8(4), 108; doi:10.3390/polym8040108

Transient Network at Large Deformations: Elastic–Plastic Transition and Necking Instability

Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
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Academic Editor: Xianqiao Wang
Received: 3 March 2016 / Revised: 16 March 2016 / Accepted: 21 March 2016 / Published: 24 March 2016
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Abstract

We theoretically investigate the mechanical response of a transient network, which is characterised by dynamically breaking and re-forming crosslinks, and accounts for the finite chain extensibility (thus permitting the large deformations to be described). We build the general theory that incorporates the widely accepted empirical model of hyper-elasticity at large deformations (the Gent model) and naturally includes the microscopic behavior of transient crosslinks under the local tension applied to them. The full analytical expression for the elastic energy, or equivalently, the constitutive relation for arbitrary deformation is derived, and then the example of uniaxial tensile strain is focused on. In this case, we show that the mechanical response depends on the ratio of the imposed strain rate and the breakage rate of the crosslink: the system flows plastically (over a yield point) when the strain rate is much smaller than the breakage rate, while it remains elastic when the strain rate is much larger than the breakage rate. There is a broad range of this transition when the elastic and plastic regions of the sample coexist, and a resulting necking instability occurs. As a generalisation, we also consider a dual transient network, with two components penetrating each other, each having its own microscopic crosslink dynamics. The two networks add their local forces and share the deformation; we find that the network with a lower breakage rate determines the global deformation of the system. View Full-Text
Keywords: transient network; large deformation; elastic–plastic transition; necking instability transient network; large deformation; elastic–plastic transition; necking instability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Meng, F.; Terentjev, E.M. Transient Network at Large Deformations: Elastic–Plastic Transition and Necking Instability. Polymers 2016, 8, 108.

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