General up to next-nearest neighbour elasticity of triangular lattices in three dimensions

Details General up to next-nearest neighbour elasticity of triangular lattices in three dimensions General up to next-nearest neighbour elasticity of triangular lattices in three dimensions

2006-02-21

arxiv.org/abs/cond-mat/0602494v1

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1098/rspa.2006.1694

We establish the most general form of the discrete elasticity of a 2D triangular lattice embedded in three dimensions, taking into account up to next-nearest neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g., red blood cell cytoskeleton) and soft matter (e.g., percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the litterature to violate rotational symmetry are in fact admissible

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