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Title: Learning the constitutive relation of polymeric flows with memory
Authors: Seryo, Naoki
Sato, Takeshi  kyouindb  KAKEN_id
Molina, John J.
Taniguchi, Takashi  kyouindb  KAKEN_id  orcid (unconfirmed)
Author's alias: 佐藤, 健
谷口, 貴志
Issue Date: 21-Jul-2020
Publisher: American Physical Society (APS)
Journal title: Physical Review Research
Volume: 2
Issue: 3
Thesis number: 033107
Abstract: We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in differential form as a function of the local stress- and strain-rate tensors. In particular, we use a Gaussian process regression to infer the constitutive relations from stress trajectories generated from small-scale (fixed strain-rate) microscopic polymer simulations. For simplicity, a Hookean dumbbell representation is used as a microscopic model, but the method itself can be generalized to incorporate more realistic descriptions. The learned constitutive relation is then used to perform macroscopic flow simulations, allowing us to update the stress distribution in the fluid in a manner that accounts for the microscopic polymer dynamics. The results using the learned constitutive relation are in excellent agreement with full multiscale simulations, which directly couple micro/macro degrees of freedom, as well as the exact analytical solution given by the Maxwell constitutive relation. We are able to fully capture the history dependence of the flow, as well as the elastic effects in the fluid. We expect the proposed learning/simulation approach to be used not only to study the dynamics of entangled polymer flows, but also for the complex dynamics of other soft-matter systems, which possess a similar hierarchy of length and timescales.
Rights: © 2020 The American Physiological Society
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
DOI(Published Version): 10.1103/PhysRevResearch.2.033107
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