Identification, based on granular micromechanics, of elastic isotropic strain gradient stiffness matrices for geometrically nonlinear deformations

Although the primacy (and utility) of higher-gradient theories are being increasingly accepted, estimates of second gradient elastic parameters are not widely available. In this talk, we present such estimates for a second-gradient continuum. These estimates 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 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 results 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.