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Localization aligned weakly periodic boundary conditions

Erik Svenning (Institutionen för tillämpad mekanik, Material- och beräkningsmekanik) ; Martin Fagerström (Institutionen för tillämpad mekanik, Material- och beräkningsmekanik) ; Fredrik Larsson (Institutionen för tillämpad mekanik, Material- och beräkningsmekanik)
International Journal for Numerical Methods in Engineering (0029-5981). Vol. 111 (2017), 5, p. 493-500.
[Artikel, refereegranskad vetenskaplig]

When computing the homogenized response of a representative volume element (RVE), a popular choice is to impose periodic boundary conditions on the RVE. Despite their popularity, it is well known that standard periodic boundary conditions lead to inaccurate results if cracks or localization bands in the RVE are not aligned with the periodicity directions. A previously proposed remedy is to use modified strong periodic boundary conditions that are aligned with the dominating localization direction in the RVE. In the present work, we show that alignment of periodic boundary conditions can also conveniently be performed on weak form. Starting from a previously proposed format for weak micro-periodicity that does not require a periodic mesh, we show that aligned weakly periodic boundary conditions may be constructed by only modifying the mapping (mirror function) between the associated parts of the RVE boundary. In particular, we propose a modified mirror function that allows alignment with an identified localization direction. This modified mirror function corresponds to a shifted stacking of RVEs, and thereby ensures compatibility of the dominating discontinuity over the RVE boundaries. The proposed method leads to more accurate results compared to using unaligned periodic boundary conditions, as demonstrated by the numerical examples.

Nyckelord: computational homogenization, weakly periodic boundary conditions, aligned periodicity, multiscale



Denna post skapades 2017-08-11.
CPL Pubid: 251075

 

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Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Material- och beräkningsmekanik (2005-2017)

Ämnesområden

Tillämpad matematik

Chalmers infrastruktur