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A second-gradient elastic (SGE) material is identified as the homogeneoussolid equivalent to a periodic planar lattice characterized by a hexagonal unitcell, which is made up of three different linear elastic bars ordered in a waythat the hexagonal symmetry is preserved and hinged at each node, so that thelattice bars are subject to pure axial strain while bending is excluded. Closedform-expressions for the identified non-local constitutive parameters areobtained by imposing the elastic energy equivalence between the lattice and thecontinuum solid, under remote displacement conditions having a dominantquadratic component. In order to generate equilibrated stresses, in the absenceof body forces, the applied remote displacement has to be constrained, thusleading to the identification in a \lq condensed' form of a higher-order solid,so that imposition of further constraints becomes necessary to fully quantifythe equivalent continuum. The identified SGE material reduces to an equivalentCauchy material only in the limit of vanishing side length of hexagonal unitcell. The analysis of positive definiteness and symmetry of the equivalentconstitutive tensors, the derivation of the second-gradient elastic propertiesfrom those of the higher-order solid in the \lq condensed' definition, and anumerical validation of the identification scheme are deferred to Part II ofthis study.

Identification of second-gradient elastic materials from planar hexagonal lattices. Part I: Analytical derivation of equivalent constitutive tensors