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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 01, 2023
- Source ID
- 10.1098/rspa.2022.0770
Entities
People
- Fabio Semperlotti
- Mehdi Jokar
- Sansit Patnaik
- Wei Ding
Organizations
- Defense Advanced Research Projects Agency
- Graduate School, Purdue University
- National Science Foundation
- Purdue University