Distillation of non-locality in porous solids

Abstract

Non-local interactions are intrinsic to multiscale heterogeneous solids. The strength of the interactions exhibits a position-dependent character whose spatial distribution strongly correlates with the underlying microstructure. In this work, a variable-order fractional calculus-based framework to distill the position-dependent non-local effects is developed. By considering the example of porous plates, theoretical and numerical analyses will illustrate the ability of variable-order mechanics to enable parsimonious and causal models via a synthetic variable-order map that naturally measures the heterogeneous non-locality induced by the microstructure; in other terms, the non-classical role of the microstructure in determining the macroscopic response. The characteristic measure for non-locality, different from the local entanglement resulting from the porosity map, allows distillation of the macroscopic non-locality, analogous to quantum non-locality distillation. The macroscopic distillation also enables the additivity of the order map, that is the ability of assembled order maps to capture the response of combined porous plates.