Abstract
In this contribution, the phase-field (PF) approach to brittle fracture is extended to adaptively refined meshes at finite strains. Such mesh refinement produces regular structured elements with hanging nodes at edges. These hanging nodes can be included to the mesh by employing the Virtual Element Method (VEM). The model performance is demonstrated by two representative numerical examples.
A dedication to Professor Peter Wriggers. I got to know you, a great man, just six months into my Doctorate study in 2012, in a great city of Vienna, which we Slovenians call Dunaj and Germans Wien. We walked around the town with your wife and Professor Korelc and we got some Sachertorte. And just 4 years later after my Promotion, I was fortunate to be invited to work as a post-doctoral student at your Institute. It was my honour working close with you for the last 5 years, discussing problems and to be your right hand in coding, it brought me great joy. I thank you for this chance you gave me, confidence in my work and that I was able work at your side all this years. I wish you health and happiness and that we can continue to closely cooperate in the future for many years to come!
—Blaž Hudobivnik
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References
Wriggers, P., Aldakheel, F., & Hudobivnik, B. (2019). Application of the virtual element method in mechanics. GAMM-Rundbriefe, 1(2019), 4–10.
Beirão Da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L. D., & Russo, A. (2013). Basic principles of virtual element methods. Mathematical Models and Methods in Applied Sciences, 23(1), 199–214.
Artioli, E., Beirão da Veiga, L., Lovadina, C., & Sacco, E. (2017). Arbitrary order 2D virtual elements for polygonal meshes: Part I, elastic problem. Computational Mechanics, 60(3), 355–377.
Wriggers, P., Rust, W. T., & Reddy, B. D. (2016). A virtual element method for contact. Computational Mechanics, 58(6), 1039–1050.
Aldakheel, F., Hudobivnik, B., Artioli, E., da Veiga, L. B., & Wriggers, P. (2020). Curvilinear virtual elements for contact mechanics. Computer Methods in Applied Mechanics and Engineering,372, 113394.
Wriggers, P., Hudobivnik, B., & Aldakheel, F. (2021). Nurbs-based geometries: A mapping approach for virtual serendipity elements. Computer Methods in Applied Mechanics and Engineering,378, 113732.
De Bellis, M. L., Wriggers, P., & Hudobivnik, B. (2019). Serendipity virtual element formulation for nonlinear elasticity. Computers & Structures,223, 106094.
Hudobivnik, B., Aldakheel, F., & Wriggers, P. (2018). A low order 3d virtual element formulation for finite elasto-plastic deformations. Computational Mechanics, 63(2), 253–269.
Aldakheel, F., Hudobivnik, B., Hussein, A., & Wriggers, P. (2018). Phase-field modeling of brittle fracture using an efficient virtual element scheme. Computer Methods in Applied Mechanics and Engineering, 341, 443–466.
Hussein, A., Aldakheel, F., Hudobivnik, B., Wriggers, P., Guidault, P.-A., & Allix, O. (2019). A computational framework for brittle crack-propagation based on efficient virtual element method. Finite Elements in Analysis and Design, 159, 15–32.
Aldakheel, F., Hudobivnik, B., & Wriggers, P. (2019). Virtual element formulation for phase-field modeling of ductile fracture. International Journal for Multiscale Computational Engineering, 17(2), 181–200.
Miehe, C., Hofacker, M., Schänzel, L.-M., & Aldakheel, F. (2015). Phase field modeling of fracture in multi-physics problems. part ii. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Computer Methods in Applied Mechanics and Engineering, 294, 486–522.
Aldakheel, F., Hudobivnik, B., & Wriggers, P. (2019). Virtual elements for finite thermo-plasticity problems. Computational Mechanics, 64(5), 1347–1360.
Wriggers, P., & Hudobivnik, B. (2017). A low order virtual element formulation for finite elasto-plastic deformations. Computer Methods in Applied Mechanics and Engineering, 327, 459–477.
Korelc, J., & Wriggers, P. (2016). Automation of finite element methods. Berlin: Springer International Publishing.
Aldakheel, F. (2016). Mechanics of nonlocal dissipative solids: Gradient plasticity and phase field modeling of ductile fracture. Stuttgart: Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart. https://doi.org/10.18419/opus-8803.
Acknowledgements
BH gratefully acknowledge financial support to this work by the German Research Foundation (DFG) with the cluster of excellence PhoenixD (EXC 2122). FA gratefully acknowledges support for this research by the “German Research Foundation” (DFG) within SPP 2020 under the project WR 19/58-2.
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Hudobivnik, B., Aldakheel, F., Wriggers, P. (2022). Adaptive Virtual Element Method for Large-Strain Phase-Field Fracture. In: Aldakheel, F., Hudobivnik, B., Soleimani, M., Wessels, H., Weißenfels, C., Marino, M. (eds) Current Trends and Open Problems in Computational Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-87312-7_20
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