Deep material networks for fiber suspensions with infinite material contrast

TL;DR

This paper introduces a novel Deep Material Network architecture called FDMN for modeling fiber suspensions with infinite contrast, achieving high accuracy in predicting effective stress responses in complex non-Newtonian fluids.

Contribution

The paper develops a new FDMN architecture with homogenization blocks for infinite contrast materials, improving modeling of fiber suspensions in non-Newtonian solvents.

Findings

FDMNs achieve validation errors below 4.31% for stress predictions.

FDMNs outperform previous machine learning models in accuracy.

The approach effectively models shear-thinning fiber suspensions across various conditions.

Abstract

We extend the laminate based framework of direct Deep Material Networks (DMNs) to treat suspensions of rigid fibers in a non-Newtonian solvent. To do so, we derive two-phase homogenization blocks that are capable of treating incompressible fluid phases and infinite material contrast. In particular, we leverage existing results for linear elastic laminates to identify closed form expressions for the linear homogenization functions of two-phase layered emulsions. To treat infinite material contrast, we rely on the repeated layering of two-phase layered emulsions in the form of coated layered materials. We derive necessary and sufficient conditions which ensure that the effective properties of coated layered materials with incompressible phases are non-singular, even if one of the phases is rigid. With the derived homogenization blocks and non-singularity conditions at hand, we present a novel DMN architecture, which we name the Flexible DMN (FDMN) architecture. We build and train FDMNs to predict the effective stress response of shear-thinning fiber suspensions with a Cross-type matrix material. For 31 fiber orientation states, six load cases, and over a wide range of shear rates relevant to engineering processes, the FDMNs achieve validation errors below 4.31% when compared to direct numerical simulations with Fast-Fourier-Transform based computational techniques. Compared to a conventional machine learning approach introduced previously by the consortium of authors, FDMNs offer better accuracy at an increased computational cost for the considered material and flow scenarios.