Describing the emerging macro-scale behavior by accounting for the micro-scale phenomena calls for microstructure-informed continuum models accounting properly for the deformation mechanisms identifiable at the micro-scale. Classical continuum theory, in contrast to the micromorphic continuum theory, is unable to take into account the effects of complex kinematics and distribution of elastic energy in internal deformation modes within the continuum material point. In this paper, we derive a geometrically nonlinear micromorphic continuum theory on the basis of granular mechanics, utilizing grain-scale deformation as the fundamental building block. The definition of objective kinematic descriptors for relative motion is followed by Piola’s ansatz for micro–macro-kinematic bridging and, finally, by a limit process leading to the identification of the continuum stiffness parameters in terms of few micro-scale constitutive quantities. A key aspect of the presented approach is the identification of relevant kinematic measures that describe the deformation of the continuum body and link it to the micro-scale deformation. The methodology, therefore, has the ability to reveal the connections between the micro-scale mechanisms that store elastic energy and lead to particular emergent behavior at the macro-scale.

通过解释微观尺度现象来描述新兴的宏观尺度行为，需要微观结构信息的连续模型正确解释微观尺度可识别的变形机制。与微形态连续体理论相比，经典连续体理论无法考虑连续体材料点内内部变形模式中复杂运动学和弹性能量分布的影响。在本文中，我们以颗粒力学为基础，利用颗粒尺度变形作为基本构建块，推导出几何非线性微晶连续体理论。相对运动的客观运动学描述符的定义之后是 Piola's ansatz 的微观-宏观运动学桥接，最后，通过一个极限过程，导致根据几个微尺度本构量识别连续体刚度参数。所提出方法的一个关键方面是确定描述连续体变形并将其与微观变形联系起来的相关运动学测量。因此，该方法有能力揭示储存弹性能量并导致宏观尺度特定紧急行为的微观机制之间的联系。