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 journalArticle

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
DOIs
StatePublished - Jan 1 2019

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Linear Elasticity
Diffuse Interface
Elasticity
elastic properties
Adaptive Refinement
Indicator function
B-spline
Far Field
Modeling
Splines
Homogenization method
Homogenization Method
Optimal Convergence Rate
splines
homogenizing
Near-field
far fields
Homogenization
Justify
Compatibility

Keywords

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

Cite this

A diffuse modeling approach for embedded interfaces in linear elasticity. / Hennig, Paul; Maier, Roland; Peterseim, Daniel; Schillinger, Dominik; Verfürth, Barbara; Kästner, Markus.

In: GAMM Mitteilungen, 01.01.2019.

Research output: Contribution to journalArticle

Hennig, Paul ; Maier, Roland ; Peterseim, Daniel ; Schillinger, Dominik ; Verfürth, Barbara ; Kästner, Markus. / A diffuse modeling approach for embedded interfaces in linear elasticity. In: GAMM Mitteilungen. 2019.
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