Granular micromechanics-based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations

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 micro-scale 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's modulus, of Poisson's ratio and of a microstructural length.