On the variational limits of lattice energies on prestrained elastic bodies

Marta Lewicka; Pablo Ochoa

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arXiv · 1403.1611

On the variational limits of lattice energies on prestrained elastic bodies

Marta Lewicka·Pablo Ochoa

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Abstract

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $Ω$. When the mesh size of the discrete lattice in $Ω$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $Γ$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$.

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Marta Lewicka, Pablo Ochoa. 2014-08-11. On the variational limits of lattice energies on prestrained elastic bodies. https://arxiv.org/abs/1403.1611

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