Circumventing mesh bias by r- and h-adaptive techniques for variational eigenfracture

  • Aurel Qinami
  • Eric Cushman Bryant
  • WaiChing Sun
  • Michael KaliskeEmail author
Computational Mechanics


This article introduces and compares mesh r- and h-adaptivity for the eigenfracture model originally proposed in Schmidt et al. (Multiscale Model Simul 7:1237–1266, 2009), Pandolfi and Ortiz (J Numer Methods Eng 92:694–714, 2012), with the goal of suppressing potential mesh bias due to the element deletion. In the r-adaptive approach, we compute the configurational force at each incremental step and move nodes near the crack tip parallel to the normalized configurational forces field such that the crack propagation direction can be captured more accurately within each incremental step. In the h-adapative approach, we introduce mesh refinement via a quad-tree algorithm to introduce more degrees of freedom within the nonlocal \(\epsilon \)-neighborhood such that a more refined crack path can be reproduced with a higher mesh resolution. Our numerical examples indicate that the r-adaptive approach is able to replicate curved cracks and complex geometrical features, whereas the h-adaptive approach is advantageous in simulating sub-scale fracture when the nonlocal regions are smaller than the un-refined coarse mesh.


Eigenerosion Mesh sensitivity R-adaptivity H-adaptivity 



This work is primarily supported by the German Research Foundation (DFG) within Research Training Group GRK 2250, Project B4. Additional funding that supports Eric Bryant and WaiChing Sun’s contributions is provided by the Earth Materials and Processes program from the Dynamic Materials and Interactions Program of the Air Force Office of Scientific Research under Grant contract FA9550-17-1-0169, and the nuclear energy university program of the Department of Energy under Grant contract DE-NE0008534. These supports are gratefully acknowledged. The views and conclusions contained in this document are those of the authors, and should not be interpreted as representing the official policies, either expressed or implied, of the sponsors, including the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute for Structural AnalysisTechnische Universität DresdenDresdenGermany
  2. 2.Department of Civil Engineering and Engineering MechanicsColumbia UniversityNew YorkUSA

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