Continuum Mechanics and Thermodynamics

, Volume 30, Issue 3, pp 485–507 | Cite as

An affine microsphere approach to modeling strain-induced crystallization in rubbery polymers

  • A. Nateghi
  • H. Dal
  • M.-A. KeipEmail author
  • C. Miehe
Original Article


Upon stretching a natural rubber sample, polymer chains orient themselves in the direction of the applied load and form crystalline regions. When the sample is retracted, the original amorphous state of the network is restored. Due to crystallization, properties of rubber change considerably. The reinforcing effect of the crystallites stiffens the rubber and increases the crack growth resistance. It is of great importance to understand the mechanism leading to strain-induced crystallization. However, limited theoretical work has been done on the investigation of the associated kinetics. A key characteristic observed in the stress–strain diagram of crystallizing rubber is the hysteresis, which is entirely attributed to strain-induced crystallization. In this work, we propose a micromechanically motivated material model for strain-induced crystallization in rubbers. Our point of departure is constructing a micromechanical model for a single crystallizing polymer chain. Subsequently, a thermodynamically consistent evolution law describing the kinetics of crystallization on the chain level is proposed. This chain model is then incorporated into the affine microsphere model. Finally, the model is numerically implemented and its performance is compared to experimental data.


Strain-induced crystallization Rubbers Network models Micromechanics 


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The financial support of the German Research Foundation (DFG) in the framework of project Mi 295/13-2 and the Cluster of Excellence EXC 310 Simulation Technology is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Mechanics, Chair IUniversity of StuttgartStuttgartGermany
  2. 2.Department of Mechanical EngineeringMiddle East Technical UniversityAnkaraTurkey

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