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A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries. (English) Zbl 1113.74076
Summary: We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach (Int. J. Numer. Meth. Engng. 2000; 48:1741).

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74E15 Crystalline structure
Software:
DECUHR; LaGriT; XFEM
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References:
[1] Sukumar, International Journal for Numerical Methods in Engineering 56 pp 2015– (2003)
[2] Kuprat, Computational Materials Science 28 pp 199– (2003)
[3] Weyer, Engineering Fracture Mechanics 69 pp 945– (2002)
[4] Moës, International Journal for Numerical Methods in Engineering 46 pp 131– (1999)
[5] Duarte, Numerical Methods for Partial Differential Equations 12 pp 673– (1996)
[6] Melenk, Computer Methods in Applied Mechanics and Engineering 139 pp 289– (1996)
[7] Daux, International Journal for Numerical Methods in Engineering 48 pp 1741– (2000)
[8] Wells, International Journal for Numerical Methods in Engineering 50 pp 2667– (2001)
[9] Moës, Engineering Fracture Mechanics 69 pp 813– (2002)
[10] Van der Giessen, International Journal of Fracture 48 pp 153– (1991) · Zbl 0759.73017
[11] Bower, Journal of the Mechanics and Physics of Solids 52 pp 1289– (2004)
[12] Chen, Computer Methods in Applied Mechanics and Engineering 193 pp 1277– (2004)
[13] Crossman, Acta Metallurgica 23 pp 425– (1975)
[14] Ghahremani, International Journal of Solids and Structures 16 pp 825– (1980) · Zbl 0515.73117
[15] Ghosh, Computational Mechanics 34 pp 510– (2004)
[16] Sukumar, International Journal for Numerical Methods in Engineering 61 pp 2045– (2004)
[17] . Clouds, cracks and FEM’s. In Recent Developments in Computational and Applied Mechanics, Reddy BD (ed.). International Center for Numerical Methods in Engineering, CIMNE, Barcelona, Spain, 1997; 302–321. · Zbl 0976.74071
[18] Oden, Computer Methods in Applied Mechanics and Engineering 153 pp 117– (1998)
[19] Taylor, Computer Methods in Applied Mechanics and Engineering 152 pp 73– (1998)
[20] Duarte, Computers and Structures 77 pp 215– (2000)
[21] Babuška, SIAM Journal on Numerical Analysis 31 pp 945– (1994)
[22] Babuška, International Journal for Numerical Methods in Engineering 40 pp 727– (1997)
[23] Duarte, Computer Methods in Applied Mechanics and Engineering 139 pp 237– (1996)
[24] Espelid, Numerical Algorithms 8 pp 201– (1994)
[25] Strouboulis, Computer Methods in Applied Mechanics and Engineering 181 pp 43– (2000)
[26] Duarte, Computer Methods in Applied Mechanics and Engineering 190 pp 2227– (2001)
[27] Chessa, International Journal for Numerical Methods in Engineering 53 pp 1957– (2002)
[28] , . Nonlinear Finite Elements for Continua and Structures. Wiley: Chichester, England, 2000. · Zbl 0959.74001
[29] Introduction to finite element methods (ASEN 5007). Course notes. Department of Aerospace Engineering Sciences, University of Colorado at Boulder, U.S.A., 2004.
[30] Babuška, Acta Numerica 12 pp 1– (2003)
[31] Ji, International Journal for Numerical Methods in Engineering 61 pp 2508– (2004)
[32] Dolbow, Finite Elements in Analysis and Design 36 pp 235– (2000)
[33] Elasticity and Anelasticity of Metals. The University of Chicago Press: Chicago, 1948.
[34] Budiansky, Journal of the Mechanics and Physics of Solids 13 pp 223– (1965)
[35] Hill, Journal of the Mechanics and Physics of Solids 13 pp 213– (1965)
[36] Mori, Acta Metallurgica 21 pp 571– (1973)
[37] Jun, International Journal of Solids and Structures 30 pp 2501– (1993)
[38] O’Connell, Journal of Geophysical Research 82 pp 5719– (1977)
[39] Fotiu, Zeitschrift fur Angewandte Mathematik und Mechanik 77 pp s465– (1997)
[40] Ghahremani, International Journal of Solids and Structures 16 pp 847– (1980) · Zbl 0515.73117
[41] Onck, International Journal of Solids and Structures 34 pp 703– (1997)
[42] Remmers, Computational Mechanics 31 pp 69– (2003)
[43] Zi, Modelling and Simulations in Materials Science and Engineering 12 pp 901– (2004)
[44] De, Computers and Structures 79 pp 2183– (2001)
[45] Griebel, SIAM Journal on Scientific Computing 22 pp 853– (2000)
[46] Strouboulis, Computer Methods in Applied Mechanics and Engineering 190 pp 4081– (2001)
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