A diffuse modeling approach for embedded interfaces in linear elasticity

Paul Hennig, Roland Maier, Daniel Peterseim, Dominik Schillinger, Barbara Verfürth, Markus Kästner

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this contribution, we present a diffuse modeling approach to embed material interfaces into nonconforming meshes with a focus on linear elasticity. For this purpose, a regularized indicator function is employed that describes the distribution of the different materials by a scalar value. The material in the resulting diffuse interface region is redefined in terms of this indicator function and recomputed by a homogenization of the adjacent material parameters. The applied homogenization method fulfills the kinematic compatibility across the interface and the static equilibrium at the interface. In addition, an hℓ-adaptive refinement strategy based on truncated hierarchical B-spline is applied to provide an appropriate and efficient approximation of the diffuse interface region. We justify mathematically and demonstrate numerically that the applied approach leads to optimal convergence rates in the far field for one-dimensional problems. A two-dimensional example illustrates that the application of the hℓ-adaptive refinement strategy allows for a clear reduction of the error in the near and far field and a good resolution of the local stress and strain fields at the interface. The use of a higher continuous B-spline basis leads to efficient computations due to the higher continuity of the diffuse interface model.

Original languageEnglish (US)
Article numbere202000001
JournalGAMM Mitteilungen
Volume43
Issue number1
DOIs
StatePublished - Mar 1 2020

Bibliographical note

Funding Information:
The authors gratefully acknowledge support from the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of nonstandard discretization methods, mechanical and mathematical analysis” under the projects KA3309/3‐2 and PE2143/2‐2. D.S. gratefully acknowledges support from the National Science Foundation via the NSF grant CISE‐1565997 and the NSF CAREER Award No. 1651577. P.H. gratefully acknowledges support from the University of Minnesota during his 3‐month research visit at the Department of Civil, Environmental, and Geo‐ Engineering.

Funding Information:
information Deutsche Forschungsgemeinschaft; KA3309/3-2; PE2143/2-2. National Science Foundation; CISE-1565997.The authors gratefully acknowledge support from the Deutsche Forschungsgemeinschaft in the Priority Program 1748 ?Reliable simulation techniques in solid mechanics. Development of nonstandard discretization methods, mechanical and mathematical analysis? under the projects KA3309/3-2 and PE2143/2-2. D.S. gratefully acknowledges support from the National Science Foundation via the NSF grant CISE-1565997 and the NSF CAREER Award No.?1651577. P.H. gratefully acknowledges support from the University of Minnesota during his 3-month research visit at the Department of Civil, Environmental, and Geo- Engineering.

Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • diffuse interface representation
  • embedded interface problems
  • homogenization
  • isogeometric analysis
  • local refinement

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