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 depen-dent continuum models. In the present work, we generalize such a micromechanical approach introducing anintrinsic 2nd gradient energy storage mechanism (resembling pantographic micromechanism), in the grain-graininteraction. Such a mechanism, represents long-range effects but could also be thought as deriving from theutilization of an actual pantographic connection between two grains in a granular metamaterial. Taking advan-tage of the homogenization approach developed in previous works, we determine the mechanical behavior of themacro-scale continuum and carry out parametric analyses with respect to the averaged intergranular distanceand with respect to the stiffness associated to the pantographic term. We show that with the inclusion of thepantographic term mentioned above, the desired thickness of the localization zone can be modeled and finelytuned successfully. We also show that the complex mechanics of load-path dependency can be predicated by themicromechanical effects and the introduced pantographic term.