Numerical multiscale solution strategy for fracturing heterogeneous materials

Computer Methods in Applied Mechanics and Engineering

Volumn 199, Issue 17-20, 2010, Pages 1100-1113

  Kaczmarczyk, Łukasz ^a   Pearce, Chris J ^a   Bićanić, Nenad ^a   de Souza Neto, Eduardo ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Arc length; Concrete; Fracturing; Hybrid trefftz finite elements; Multigrid

Indexed keywords

CARBON DIOXIDE ARC WELDING; CONCRETES; FRACTURING (FOSSIL FUEL DEPOSITS); NEWTON-RAPHSON METHOD;

ARC LENGTH; COMPUTATIONAL HOMOGENIZATION; CONVERGENCE PROPERTIES; CONVERGENCE TOLERANCES; HETEROGENEOUS MATERIALS; MULTI-GRID; MULTI-SCALE MODELLING; PARALLEL IMPLEMENTATIONS;

ITERATIVE METHODS;

EID: 79955741342     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.11.018     Document Type: Article

References (31)

1. A. Matuszak, Partial Material Replacement without Stress Redistribution in Plane Problems of Elasticity, PhD Thesis, Cracow University of Technology, 2003 (in Polish).
2. C. Miehe, C.G. Bayreuther, On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers, Int. J. Numer. Methods Engrg. 71 (2007) 1135-1180.
3. J.A. Teixeira de Freitas, Formulation of elastostatic hybrid-Trefftz stress elements, Comput. Methods Appl. Mech. Engrg. 153 (1998) 27-151.
4. M.R.A. Van Vliet, Size Effect in Tensile Fracture of Concrete and Rock, PhD Thesis, Technische Universiteit Delft, 2000.
5. V. Kouznetsova, M.G.D. Geers, W.A.M. Brekelmans, Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, Int. J. Numer. Methods Engrg. 54 (2002) 1235-1260.
6. G. Alfano, M.A. Crisfield, Solution strategies for the delamination analysis based on a combination of local-control arc-length and line searches, Int. J. Numer. Methods Engrg. 58 (2003) 999-1048.
7. T. Belytschko, S. Loehnert, J.-H. Song, Multiscale aggregating discontinuities: a method for circumventing loss of material stability, Int. J. Numer. Methods Engrg. 73 (2008) 869-894.
8. J.C. Michel, H. Moulinec, P. Suquet, Effective properties of composite materials with periodic microstructure: a computational approach, Comp. Methods Appl. Mech. Engrg. 172 (1999) 109-143.
9. C. Miehe, A. Koch, Computational micro-to-macro transitions of discretized microstructures undergoing small strains, Arch. Appl. Mech. 72 (2002) 300-317.
10. I.M. Gitman, H. Askes, L.J. Sluys, Coupled-volume multi-scale modelling of quasibrittle material, Eur. J. Mech. A/Solids 27 (2008) 302-327.
11. I.M. Gitman, H. Askes, L.J. Sluys, Representative volume: existence and size determination, Engrg. Fract. Mech. 74 (2007) 2518-2534.
12. Ł. Kaczmarczyk, C.J. Pearce, N. Bićanić, Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization, Int. J. Numer. Methods Engrg. 74 (2007) 506-522.
13. Ł. Kaczmarczyk, C.J. Pearce, A corotational hybrid-Trefftz stress formulation for modelling cohesive cracks, Comp. Methods Appl. Mech. Engrg. 198 (2009) 1298-1310.
14. F. Feyel, A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua, Comput. Methods Appl. Mech. Engrg. 192 (2003) 3233-3244.
15. M.G.A. Tijssens, On the Cohesive Surface Methodology for Fracture of Brittle Heterogeneous Solids, PhD Thesis, Technische Universiteit Delft, 2001.
16. M.G.D. Geers, Enhanced solution control for physically and geometrically nonlinear problems Part I. - the subplane control approach, Int. J. Numer. Methods Engrg. 46 (1999) 177-204.
17. S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L. Curfman McInnes, B.F. Smith, H.Zhang, PETSc Web page, , 2009.
18. S. Balay, K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L. Curfman McInnes, B.F. Smith, H. Zhang, PETSc Users Manual, ANL-95/11 - Revision 3.0.0, Argonne National Laboratory, 2008.
19. S. Balay, W.D. Gropp, L. Curfman McInnes, B.F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in: E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.), Modern Software Tools in Scientific Computing, Birkhäuser Press, 1997, pp. 163-202.
20. Y. Saad, Iterative Methods for Sparse Linear Systems, PWS, 1996.
21. J. Xu, An introduction to multigrid convergence theory, in: Iterative Methods in Scientific Computing (Hong Kong, 1995), Springer, Singapore, 1997, pp. 169-241.
22. Mark F. Adams, A distributed memory unstructured gauss-seidel algorithm for multigrid smoothers, in: Proceedings of the 2001 ACM/IEEE Conference on Supercomputing (CDROM), 2001.
23. A. Hillerborg, M. Modeer, P.E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement Concrete Res. 6 (6) (1976) 773-782.
24. M. Ainsworth, Essential boundary conditions and multi-point constraints in finite element analysis, Comp. Methods Appl. Mech. Engrg. 190 (2001) 6323-6339.
25. V. Kompiš, F. Konol', M. Vaško, Trefftz-polynomial reciprocity based FEM formulations, Comp. Assist. Mech. Engrg. Sci. 8 (2/3) (2001) 385-398.
26. J.C. Walraven, Aggregate Interlock: A Theoretical and Experimental Analysis, PhD, Delft University of Technology, 1980.
27. R.A. Toupin, Elastic materials with couple-stresses, Arch. Ration. Mech. Anal. 11 (1968) 385-413.
28. J.Y. Shu, W.E. King, N.A. Fleck, Finite elements for materials with strain gradient effects, Int. J. Numer. Methods Engrg. 44 (1999) 373-391.
29. E.M. Kasparek, An efficient triangular plate element with C-1-continuity, Int. J. Numer. Methods Engrg. 73 (2008) 1010-1026.
30. D. Markovic, A. Ibrahimbegovic, Complementary energy based FE modelling of coupled elasto-plastic and damage behavior for continuum microstructure computations, Comp. Methods Appl. Mech. Engrg. 195 (2006) 5077-5093.
31. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, Butterworth-Heinemann, 2005.