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

• Published in: International journal of fracture Vol. 220; no. 2; pp. 129 - 142
• Main Authors: Qinami, Aurel, Bryant, Eric Cushman, Sun, WaiChing, Kaliske, Michael
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2019; Springer Nature B.V; Springer
• Subjects: Algorithms; Automotive Engineering; Bias; Characterization and Evaluation of Materials; Chemistry and Materials Science; Civil Engineering; Classical Mechanics; Computational Mechanics; Computer simulation; Crack propagation; Crack tips; Deletion; eigenerosion; Finite element method; Fracture mechanics; Grid refinement (mathematics); h-adaptivity; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Materials Science; Mathematical analysis; Mechanical Engineering; mechanics; mesh sensitivity; r-adaptivity; Mesh sensitivity; H-adaptivity; R-adaptivity; Eigenerosion
• ISSN: 0376-9429; 1573-2673; 1573-2673
• DOI: 10.1007/s10704-019-00349-x

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 ϵ -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.