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An atomistic-based finite deformation membrane for single layer crystalline films. (English) Zbl 1006.74061
Summary: We present a general methodology to develop hyperelastic membrane models applicable to crystalline one-atom thick films. In this method, we propose an extension of Born rule based on exponential map. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements.

MSC:
74K15 Membranes
74K35 Thin films
74S05 Finite element methods applied to problems in solid mechanics
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