Hyperelasticity governs dynamic fracture at a critical length scale

Abstract

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.

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Figure 1: The simulation geometry with the lattice orientation and the weak layer.
Figure 2: Hyperelastic zone and the associated change in energy flow near the crack tip.
Figure 3: Change of crack speed with the onset strain of hyperelasticity.
Figure 4: Intersonic mode I crack motion and supersonic mode II crack motion.
Figure 5: Scaling law for the characteristic length associated with energy transport near the crack tip.

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Acknowledgements

F.F.A. acknowledges the generous support provided by the Humboldt Research Award for Senior US Scientists.

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Correspondence to Huajian Gao.

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Buehler, M., Abraham, F. & Gao, H. Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426, 141–146 (2003). https://doi.org/10.1038/nature02096

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