Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics

Describing the emerging macro-scale behavior by accounting for the micro-scalephenomena calls for microstructure-informed continuum models accounting properlyfor the deformation mechanisms identifiable at the grain-scale. Classical continuumtheory, in contrast to the micromorphic continuum theory, is unable to take into accountthe effects of complex kinematics and distribution of elastic energy in internaldeformation modes within the continuum material point. In this paper, we derive ageometrically non-linear micromorphic continuum theory on the basis of granularmechanics, utilizing grain-scale deformation as the fundamental building block. Thedefinition of objective kinematic descriptors for relative motion is followed by Piola'sansatz for micro-macro kinematic bridging and, finally, by a limit process leading to theidentification of the continuum stiffness parameters in terms of few micro-scaleconstitutive quantities. A key aspect of the presented approach is the identification ofrelevant kinematic measures that describe the deformation of the continuum body andlink it to the micro-scale deformation. The methodology, therefore, has the ability toreveal the connections between the micro-scale mechanisms that store elastic energyand lead to particular emergent behavior at the macro-scale.