Green’s functions and integral representation of generalized continua: the case of orthogonal pantographic lattices

This paper shows how the classical representation techniques for solution of elasticity problems, based on Green’s functions, can be generalized to second-gradient continua focusing specific case pantographic lattices. As these last are strongly anisotropic, fundamental solutions isotropic involving bi-Helmholtz-type operators not applicable. More specifically we establish analytical linearized equations governing equilibrium 2D in neighbourhood reference configuration. Moreover, by means found novel it is shown that possible solve aforesaid using Fredholm integral equations. It seen an approximated standard bias test judiciously solutions. The micro-macro-asymptotic identification allows a clear and satisfactory physical interpretation obtained results.