×

A mesh adaptation procedure for periodic domains. (English) Zbl 1235.74273

Summary: In this paper, an original technique is developed in order to build adaptive meshes on periodic domains. The new approach has the important property that it is code-reused. The procedure is used against three different algorithms, namely, MAdLib. None of the latter algorithms needs to be adapted before it is applied to periodic domains. Some examples of adaptation are presented based on analytical, isotropic and anisotropic mesh-size fields. Periodicity in translation and rotation both are considered. Finally, the mesh adaptation strategy is used in order to reduce the computational cost of a prediction of strain heterogeneity throughout a periodic polycrystalline aggregate deforming by dislocation slip.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E15 Crystalline structure
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Software:

MAdLib
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gonzalez, Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models, Journal of the Mechanics and Physics of Solids 52 (7) pp 1573– (2004) · Zbl 1103.74020 · doi:10.1016/j.jmps.2004.01.002
[2] Kouznetsova, Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy, Computer Methods in Applied Mechanics and Engineering 193 (48-51) pp 5525– (2004) · Zbl 1112.74469 · doi:10.1016/j.cma.2003.12.073
[3] Delannay, Influence of grain shape on the planar anisotropy of rolled steel sheets-evaluation of three models, Computational Materials Science 45 (3) pp 739– (2009) · doi:10.1016/j.commatsci.2008.06.013
[4] Zhao, Influence of in-grain mesh resolution on the prediction of deformation textures in fcc polycrystals by crystal plasticity fem, Acta Materialia 55 (7) pp 2361– (2007) · doi:10.1016/j.actamat.2006.11.035
[5] Kaczmarczyk, Scale transition and enforcement of rve boundary conditions in second-order computational homogenization, International Journal for Numerical Methods in Engineering 74 (3) pp 506– (2008) · Zbl 1159.74403 · doi:10.1002/nme.2188
[6] Béchet, A stable lagrange multiplier space for stiff interface conditions within the extended finite element method, International Journal for Numerical Methods in Engineering 78 pp 931– (2009) · Zbl 1183.74259 · doi:10.1002/nme.2515
[7] Wenk, Texture and Anisotropy, Preferred Orientations in Polycrystals and their Effect on Materials Properties (1998)
[8] Resk, Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations, Modelling and Simulation in Materials Science and Engineering 17 (7) pp 075012– (2009) · doi:10.1088/0965-0393/17/7/075012
[9] Kuroda, An alternative treatment of phenomenological higher-order strain-gradient plasticity theory, International Journal of Plasticity (2009)
[10] Bernacki, Level set framework for the numerical modelling of primary recrystallization in polycrystalline materials, Scripta Materialia 58 (12) pp 1129– (2008) · doi:10.1016/j.scriptamat.2008.02.016
[11] Melchior, A texture discretization technique adapted to polycrystalline aggregates with non-uniform grain size, Computational Materials Science 37 (4) pp 557– (2006) · doi:10.1016/j.commatsci.2005.12.002
[12] George, Encyclopedia of Computational Mechanics (2004)
[13] Alauzet F Frey PJ Estimateur d’erreur géométrique et métriques anisotropes pour l’adaptation de maillage. partie 1: aspects théoriques 2003
[14] Leservoisier D George P-L Dervieux A Métrique continue et optimisation de maillage 2001
[15] Frey, Maillages: applications aux éléments finis (1999)
[16] Compère, A mesh adaptation framework for dealing with large deforming meshes, International Journal for Numerical Methods in Engineering (2000) · Zbl 1188.74093
[17] Li, 3d anisotropic mesh adaptation by mesh modification, Computer Methods in Applied Mechanics and Engineering 194 pp 4915– (2005) · Zbl 1090.76060 · doi:10.1016/j.cma.2004.11.019
[18] Compère, Proceedings of 17th International Meshing Roundtable 3 pp 213– (2008) · doi:10.1007/978-3-540-87921-3_13
[19] Dobrzynski C Frey P Anisotropic delaunay mesh adaptation for unsteady simulations · Zbl 1292.76041
[20] Frey PJ Yams: A fully automatic adaptive isotropic surface remeshing procedure 2001
[21] George P-L Tet meshing: construction, optimization and adaptation
[22] Mishra, On the widths of orientation gradient zones adjacent to grain boundaries, Scripta Materialia 61 (3) pp 273– (2009) · doi:10.1016/j.scriptamat.2009.03.062
[23] Delannay, Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons, International Journal of Plasticity 22 (10) pp 1879– (2006) · Zbl 1136.74375 · doi:10.1016/j.ijplas.2006.01.008
[24] Hughes TJR Consider a spherical cow-conservation of geometry in analysis: Implications for computational methods in engineering
[25] 2008
[26] Kuroda, Effects of texture on shear band formation in plane strain tension/compression and bending, International Journal of Plasticity 23 (2) pp 244– (2007) · Zbl 1127.74317 · doi:10.1016/j.ijplas.2006.03.014
[27] Delannay, Cpfem investigation of the effect of grain shape on the planar anisotropy and the shear banding of textured metal sheets, Ceramic Transactions 201 pp 745– (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.