Micro-mechano-morphology-informed continuum damage modeling with intrinsic 2nd gradient (pantographic) grain–grain interactions

In a previous work, we have shown that a granular micromechanics approach can lead to load path dependent continuum models. In the present work, we generalize such a micromechanical approach introducing an intrinsic 2nd gradient energy storage mechanism (resembling pantographic micromechanism), in the grain–grain interaction. Such a mechanism, represents long-range effects but could also be thought as deriving from the utilization of an actual pantographic connection between two grains in a granular metamaterial. Taking advantage of the homogenization approach developed in previous works, we determine the mechanical behavior of the macro-scale continuum and carry out parametric analyses with respect to the averaged intergranular distance and with respect to the stiffness associated to the pantographic term. We show that with the inclusion of the pantographic term mentioned above, the desired thickness of the localization zone can be modeled and finely tuned successfully. We also show that the complex mechanics of load-path dependency can be predicated by the micromechanical effects and the introduced pantographic term.