A new technique has been developed to study fracture in nanomaterials, in which quantum and continuum mechanics are coupled.  A key feature of the method is that broken bonds are identified by  sharp drops in the quantum-mechanical electron densities at crack tips.  As fracture occurs, the tip positions and crack paths are updated in the continuum mechanics, from the broken bonds in the quantum mechanical (QM) models.  As the simulations proceed, the QM models are centered on the crack tips to adaptively follow their courses, making it possible to trace paths with complicated geometries.  The method is applied to the study of graphene fracture.  The simulations indicate that cracks initially parallel to the zigzag edge propagate self-similarly, while armchair cracks advance in an irregular manner.  The associated critical stress intensity factors were found to be 4.21 and 3.71 MPa m1/2, respectively, which are about 10% that for mild steel.  The displacement fields necessary to make these estimates could only have been applied accurately to sheets that are much too large for QM models, while the use of quantum mechanics is essential for the accurate modeling of the propagation of the crack tips.

Coupled quantum and continuum mechanics for the study of graphene fracture

244th National Meeting (2012)

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