Department of Mechanics: Seminar: Abstract Henys 2019: Difference between revisions

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=== Homogenizace a více-škálové modelování s libovolnou MKP sítí reprezentativního modelu ===
=== Homogenization and multi-scale modeling with arbitrary finite element mesh of representative volume element ===


==== [https://www.researchgate.net/profile/Petr_Henys Petr Henyš], Odborný asistent, Katedra technologií a struktur, Fakulta textilní, Technická univerzita v Liberci ====
==== [https://www.researchgate.net/profile/Petr_Henys Petr Henyš], Researcher, Department of Technologies and Structures, Faculty of Textile Engineering, Technical University of Liberec ====


'''Místnost B-366, [https://goo.gl/maps/9fgUfCGjn2k Fakulta stavební, ČVUT v Praze]'''  
'''Room B-366, [https://goo.gl/maps/9fgUfCGjn2k Fakulta stavební, CTU in Prague]'''  


'''Středa, 17. dubna 2019, 10:00-11:00'''  
'''Wednesday, 17 April 2019, 10:00-11:00'''  


Periodické okrajové podmínky (POP) jsou často využívány pro výpočet homogenizovaných vlastností média pomocí metody konečných prvků (MKP). Pro implementaci POP je optimální aby MKP síť byla konformní na okrajích, kde se předepisuje POP, nicméně pro geometricky a materiálově složitější modely je obtížné požadavek POP dodržet současnými technikami síťování MKP modelů. Tato studie je zaměřena na implementaci POP bez požadavku na konformitu okrajů MKP sítě. Představená metoda vychází z kombinace Nitscheho metody umožňující slabou implementaci Dirichletových OP a metody pro implementaci kontaktních vazeb mezi tělesy. Navržená metoda je otestována v sérii numerických příkladů a porovnána s referenčními technikami (mortar a bezsíťová metoda). Rozdíly v homogenizovaných konstantách elasticity testovaných modelů se pohybují do 1 %. Navrhovaná metoda nezvyšuje počet stupňů volnosti oproti mortar metodě a nevyžaduje manuální odhad řádu interpolace jako bezsíťová technika.
Periodic boundary conditions (PBCs) are often used to estimate the homogenized properties of a media using the finite element method (FEM). The optimal treatment of PBCs requires the finite element mesh to be conformal on the boundaries where the PBCs are prescribed. Nevertheless, it is difficult to enforce PBCs on complex geometrical domains with multiple material phases with current finite element meshing algorithms. This study focuses on the treatment of PBCs on arbitrary meshes without conformal boundaries. The presented method for treatment of PBCs is based on the Nitsche's method, which allows imposing Dirichlet boundary conditions weakly as well as interface contact constraints. The proposed method is tested and compared with the state-of-the-art methods (mortar and meshless methods) within a set of numerical benchmarks. The resultant homogenized properties differ up to 1 % and can be considered negligible, while the Nitsche's method does not increase the size of the model and does not require manual tuning of additional parameters, unlike the meshless method.

Revision as of 09:44, 5 April 2019

Homogenization and multi-scale modeling with arbitrary finite element mesh of representative volume element

Petr Henyš, Researcher, Department of Technologies and Structures, Faculty of Textile Engineering, Technical University of Liberec

Room B-366, Fakulta stavební, CTU in Prague

Wednesday, 17 April 2019, 10:00-11:00

Periodic boundary conditions (PBCs) are often used to estimate the homogenized properties of a media using the finite element method (FEM). The optimal treatment of PBCs requires the finite element mesh to be conformal on the boundaries where the PBCs are prescribed. Nevertheless, it is difficult to enforce PBCs on complex geometrical domains with multiple material phases with current finite element meshing algorithms. This study focuses on the treatment of PBCs on arbitrary meshes without conformal boundaries. The presented method for treatment of PBCs is based on the Nitsche's method, which allows imposing Dirichlet boundary conditions weakly as well as interface contact constraints. The proposed method is tested and compared with the state-of-the-art methods (mortar and meshless methods) within a set of numerical benchmarks. The resultant homogenized properties differ up to 1 % and can be considered negligible, while the Nitsche's method does not increase the size of the model and does not require manual tuning of additional parameters, unlike the meshless method.

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