An atomistic-based finite deformation membrane for crystalline films one atom thick

A general methodology to develop hyper-elastic membrane models equivalent to crystalline films one atom thick is presented. This membrane theory is used to study the mechanics of carbon nanotubes. The method relies on an extension of the Born based on the exponential map. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical models, the exponential map is locally approximated. Numerical simulations of a membrane for carbon nanotubes discretized by finite elements are given.

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