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特別講演

講師:Peter Wriggers 教授
(Leibniz Universitt Hannover, Germany)

講演タイトル:
3D error controlled adaptive multiscale extended finite element methods for crack simulations

開催日:5月26日
時間:16:15〜17:15(予定)
参加費:無料


要旨

3D error controlled adaptive multiscale extended finite element methods for crack simulations

P. Wriggers
S. Loehnert, D.S. Mueller-Hoeppe, M. Holl, C. Hoppe, H. Clasen

Institute of Continuum Mechanics, Leibniz Universitt Hannover, Germany

Key Words: multiscale, crack propagation, crack coalescence, adaptive, error control

ABSTRACT

The multiscale projection method [1] designed for localization phenomena and domains with stress concentrations and high stress gradients is extended to crack propagation and crack coalescence as well as to three dimensions. Typical and important industrial applications are brittle ceramic materials where microcrack nucleation and propagation in the vicinity of propagating macrocracks can be observed.

Within the multiscale XFEM framework crack propagation as well as crack coalescence is computed accurately on the microscale. The possible coalescence of micrcracks and macrocracks necessitates the projection of new crack configurations between the scales. On the macroscale the macroscopic boundary value problem needs to be solved incorporating all the necessary information from the microstructural features. Crack propagation automatically leads to a changing fine scale domain resulting in a model adaption. Within these simulations the corrected XFEM [2,3] was applied that modifies the ramp function, blending out the crack tip enrichment functions without violating the partition of unity concept. This is necessary on the macroscale to account for an accurate description of microcracks and macrocracks and their coalescence.

To control the accuracy of the simulations, on the fine scale an error controlled adaptive mesh refinement strategy is applied. The error estimation is based on the well known Zienkiewicz and Zhu method. However, the ansatz for the enhanced smoothed stress eld calculated by a stress projection needs to be modified to accurately account for possible stress singularities as well as stress kinks and jumps. Here, also for the enhanced smoothed stresses a special XFEM approach is chosen.

REFERENCES

[1] S. Loehnert and T. Belytschko: A multiscale projection method for macro/microcrack simulations. Int. J. Numer. Meth. Engng., Vol. 71, 1466-1482, 2007.
[2] S. Loehnert, D.S. Mueller-Hoeppe and P. Wriggers: 3D corrected XFEM approach and extension to nite deformation theory. Int. J. Numer. Meth. Engng., DOI:10.1002/nme.3045, 2010.
[3] T.-P. Fries: A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Meth. Engng., Vol. 75, 503-532, 2008.