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Title: A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

Abstract

Here, we introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, whilemore » the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.« less

Authors:
 [1];  [2]; ORCiD logo [2]
+ Show Author Affiliations
  1. McMaster Univ., Hamilton, ON (Canada)
  2. Columbia Univ., New York, NY (United States)
Publication Date:
Research Org.:
Columbia Univ., New York, NY (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); National Science Foundation (NSF)
OSTI Identifier:
1801238
Alternate Identifier(s):
OSTI ID: 1566184
Grant/Contract Number:  
NE0008534; W911NF-18-2-0306; FA9550-17-1-0169; CMMI-1846875
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 357; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; engineering; mathematics; mechanics; adaptive meshing; configurational force; regularization; poromechanics; lie-algebra interoplation

Citation Formats

Na, SeonHong, Bryant, Eric C., and Sun, WaiChing. A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables. United States: N. p., 2019. Web. doi:10.1016/j.cma.2019.112572.
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Na, SeonHong, Bryant, Eric C., & Sun, WaiChing. A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables. United States. https://doi.org/10.1016/j.cma.2019.112572
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Na, SeonHong, Bryant, Eric C., and Sun, WaiChing. Tue . "A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables". United States. https://doi.org/10.1016/j.cma.2019.112572. https://www.osti.gov/servlets/purl/1801238.
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@article{osti_1801238,
title = {A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables},
author = {Na, SeonHong and Bryant, Eric C. and Sun, WaiChing},
abstractNote = {Here, we introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.},
doi = {10.1016/j.cma.2019.112572},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 357,
place = {United States},
year = {Tue Aug 13 00:00:00 EDT 2019},
month = {Tue Aug 13 00:00:00 EDT 2019}
}
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