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Nature 426, 141-146 (13 November 2003) | doi:10.1038/nature02096; Received 17 April 2003; Accepted 19 September 2003

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Hyperelasticity governs dynamic fracture at a critical length scale

Markus J. Buehler1,3, Farid F. Abraham2,3 & Huajian Gao1,3

  1. Max Planck Institute for Metals Research, Heisenbergstrasse 3, 70569 Stuttgart, Germany
  2. IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA
  3. These authors contributed equally to this work

Correspondence to: Huajian Gao1,3 Email: hjgao@mf.mpg.de

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The elasticity of a solid can vary depending on its state of deformation. For example, metals will soften and polymers may stiffen as they are deformed to levels approaching failure. It is only when the deformation is infinitesimally small that elastic moduli can be considered constant, and hence the elasticity linear. Yet, many existing theories model fracture using linear elasticity, despite the fact that materials will experience extreme deformations at crack tips. Here we show by large-scale atomistic simulations that the elastic behaviour observed at large strains—hyperelasticity—can play a governing role in the dynamics of fracture, and that linear theory is incapable of fully capturing all fracture phenomena. We introduce the concept of a characteristic length scale for the energy flux near the crack tip, and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale.

  1. Max Planck Institute for Metals Research, Heisenbergstrasse 3, 70569 Stuttgart, Germany
  2. IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA
  3. These authors contributed equally to this work

Correspondence to: Huajian Gao1,3 Email: hjgao@mf.mpg.de