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Polymer Networks with Slip-links: 2. Constitutive Equations for a Cross-linked Network

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Abstract

Stress–strain relations are derived for the mechanical response of elastomers at arbitrary three-dimensional deformations with finite strains. An elastomer is treated as an incompressible network of chains bridged by permanent (chemical cross-links and physical cross-links whose lifetime exceeds the characteristic time of deformation) and temporary (entanglements modeled as slip-links) junctions. Two types of chains are introduced in the network to distinguish between permanent and temporary nodes. Type-I chains have free ends, and their motion at the micro-level is constrained by a random number of slip-links. Type-II chains are Gaussian chains permanently connected to the network. Concentration of type-I chains is fixed, while the number of type-II chains per unit volume can change under deformation. The governing equations involve two (networks with constant concentrations of type-II chains) or three (networks where the content of type-II chains is affected by mechanical factors) material parameters. These parameters are found by fitting observations on rubbers, thermoplastic–elastomers, and thermoplastic-elastomer composites. Good agreement is demonstrated between the experimental data in uniaxial tensile tests and the results of numerical simulation at elongations up to 1,000%. It is shown that the adjustable parameters are affected by chemical composition and molecular architecture of polymers in a physically plausible way.

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Authors and Affiliations

  1. Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel

    A. D. Drozdov

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  1. A. D. Drozdov
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Correspondence to A. D. Drozdov.

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Communicated by A. DeSimone

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Drozdov, A.D. Polymer Networks with Slip-links: 2. Constitutive Equations for a Cross-linked Network. Continuum Mech. Thermodyn. 18, 171–193 (2006). https://doi.org/10.1007/s00161-006-0021-x

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  • DOI: https://doi.org/10.1007/s00161-006-0021-x

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