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The configurational-forces view of the nucleation and propagation of fracture and healing in elastomers as a phase transition

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Abstract

In a recent contribution, Kumar et al. (J Mech Phys Solids 112:523–551, 2018) have introduced a macroscopic theory aimed at describing, explaining, and predicting the nucleation and propagation of fracture and healing in elastomers undergoing arbitrarily large quasistatic deformations. The purpose of this paper is to present an alternative derivation of this theory—originally constructed as a generalization of the variational theory of brittle fracture of Francfort and Marigo (J Mech Phys Solids 46:1319–1342, 1998) to account for physical attributes innate to elastomers that have been recently unveiled by experiments at high spatio-temporal resolution—cast as a phase transition within the framework of configurational forces. A second objective of this paper is to deploy the theory to probe new experimental results on healing in silicone elastomers.

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Notes

  1. In addition to elastic deformations, viscous deformations are likely to play a role in the nucleation and propagation of fracture and healing in elastomers; see, e.g., Mullins (1959) and Kumar et al. (2017).

  2. The extension of the present formulation to the case of any number of phases is straightforward.

  3. Throughout this work, we focus on isothermal processes.

  4. The partial derivative with respect to the configurational variable z should be interpreted as a constrained derivative since \(0\le z \le 1\).

  5. For instance, it is possible that the elasticity—and not just the toughness—of the elastomer also evolves with the cumulative history of fracture and healing.

  6. In addition to internal microscopic defects throughout its volume, a given piece of elastomer will feature as well surface microscopic defects on its boundary. Depending on the geometry of the piece and the applied loading conditions, accounting for those may also be essential in order to describe correctly the nucleation of macroscopic fracture.

  7. Here, it is important to emphasize that the PDMS elastomer used in the experiment, featuring a 30:1 ratio of base to curing agent, is a solid capable of some viscous dissipation. Consequently, its idealization as a nonlinear elastic solid in the theory may cause some disagreement between the predictions from the theory and the experimental observations.

  8. We recall that smaller positive values in the healing branch of the toughness function \(k(\dot{z},\alpha , t^*)\) imply that the material exhibits a higher resistance to heal. Again, non-positive values imply that healing is prohibited altogether; see Remark 4 in Kumar et al. (2018).

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Acknowledgements

Support for this work by the National Science Foundation through the Grant DMS–1615661 is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois, Urbana–Champaign, Urbana, IL, 61801-2352, USA

    Aditya Kumar & Oscar Lopez-Pamies

  2. Department of Aerospace and Engineering Mechanics, The University of Texas at Austin, Austin, TX, 78712–1221, USA

    K. Ravi-Chandar

Authors
  1. Aditya Kumar
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  2. K. Ravi-Chandar
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  3. Oscar Lopez-Pamies
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Correspondence to Oscar Lopez-Pamies.

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Kumar, A., Ravi-Chandar, K. & Lopez-Pamies, O. The configurational-forces view of the nucleation and propagation of fracture and healing in elastomers as a phase transition. Int J Fract 213, 1–16 (2018). https://doi.org/10.1007/s10704-018-0302-y

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