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Although the primacy and utility of higher-gradient theories are being increasingly accepted, values of second gradient elastic parameters are not widely available due to lack of generally applicable methodologies. In this paper, we present such values for a second-gradient continuum. These values are obtained in the framework of finite deformations using granular micromechanics assumptions for materials that have granular textures at some ‘microscopic’ scale. The presented approach utilizes so-called Piola’s ansatz for discrete-continuum identification. As a fundamental quantity of this approach, an objective relative displacement between grain-pairs is obtained and deformation energy of grain-pair is defined in terms of this measure. Expressions for elastic constants of a macroscopically linear second gradient continuum are obtained in terms of the microscale grain-pair parameters. Finally, the main result is that the same coefficients, both in the 2D and in the 3D cases, have been identified in terms of Young’smodulus, of Poisson’s ratio and of a microstructural length. 

In order to get detailed information about the mechanical behavior of pantographic elementary substructure and elements, small-scale specimens were sintered using polyamide powder, constituted by three orthogonal pairs of beams interconnected through pivots forming pantographic cells. The mechanical properties of interconnecting pivots and constituting beams are investigated by comparing experimental evidence with an enhanced Piola–Hencky model. The careful agreement between experimental and predicted results allows us to estimate: (i) the macro-shear stiffness of interconnecting pivots (corresponding to micro-torsional stiffness), (ii) extensional stiffness and (iii) bending stiffness of constituting beams.