1. XI International Conference on COMPUTATIONAL PLASTICITY FUNDAMENTALS AND APPLICATIONS COMPLAS XI 7-9 September 2011 Barcelona - Spain Multiscale Modelling of Masonry Structures under Extreme Loading B A Izzuddin and L Macorini Department of Civil and Environmental Engineering Imperial College London, UK

2. Outline Advanced models for brick-masonry Advanced models for brick-masonry Multiscale modelling approaches Multiscale modelling approaches Domain partitioning approach Domain partitioning approach 2/23 Multiscale Modelling of Masonry Structures under Extreme Loading 2/23 3D mesoscale model for nonlinear analysis 3D mesoscale model for nonlinear analysis Conclusions Conclusions

3. Macroscale model Equivalent material approach Mesoscale model Two-material approach Structural scale Mesoscale scale Microscale scale Advanced models for brick-masonry 3/23 Multiscale Modelling of Masonry Structures under Extreme Loading 3/23

4. Macroscale model Equivalent material approach Identification of material properties for macro-model Advanced models for brick-masonry 4/23 Multiscale Modelling of Masonry Structures under Extreme Loading 4/23

5. Multiscale approaches for masonry Homogenisation approach Homogenisation approach Nested multiscale - FE 2 Nested multiscale - FE 2 approach approach Basic cell (RVE)Homogenised continuum Homogenisation 5/23 Multiscale Modelling of Masonry Structures under Extreme Loading 5/23 ( Massart, 2007)

6. Multiscale approaches for masonry 6/23 Multiscale Modelling of Masonry Structures under Extreme Loading 6/23 Not effective for representing masonry when: the characteristic length of FEs at structural scale and RVE linear dimension are close the characteristic length of FEs at structural scale and RVE linear dimension are close complex texture (multi-leaf masonry etc.) complex texture (multi-leaf masonry etc.) FE 2 approach

7. Mesoscale partitioned modelling Structural scale 3D brick/2D interface elements An advanced 3D mesoscale model incorporated into a multi-scale formulation Partitioning approach with macro-elements for masonry Partitioning approach with macro-elements for masonry Parallel computing Parallel computing 7/23 Multiscale Modelling of Masonry Structures under Extreme Loading 7/23 Mesoscale

8. Mesoscale partitioned modelling An advanced 3D mesoscale model incorporated into a multi-scale formulation 8/23 Multiscale Modelling of Masonry Structures under Extreme Loading 8/23

9. 2D nonlinear interface element      <0 G f,II u x(y)  tan   C G f,I uzuz tt    cc    uzuz GcGc 3D mesoscale model for nonlinear analysis under extreme loading Shear test Compression test Multi-surface nonassociated Multi-surface nonassociated plasticity plasticity Geometric nonlinearity Geometric nonlinearity 9/23 Multiscale Modelling of Masonry Structures under Extreme Loading 9/23

10. In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) J4DJ5D p v =0.3 MPa mortar interface brick interface 3D mesoscale model for nonlinear analysis under extreme loading 10/23 Multiscale Modelling of Masonry Structures under Extreme Loading 10/23

11. In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) J4DJ5D Wpl1 Wpl2 p v =0.3 MPa 3D mesoscale model for nonlinear analysis under extreme loading 11/23 Multiscale Modelling of Masonry Structures under Extreme Loading 11/23

12. In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) Wpl1 Wpl2 12/23 Nonlinear Analysis of Masonry Structures using Mesoscale Partitioned Modelling 12/23 3D mesoscale model for nonlinear analysis under extreme loading

13. Out-of-plane behaviour Chee Liang, N.G. (1996) Wpl1Wpl1Wpl1 3D mesoscale model for nonlinear analysis under extreme loading 13/23 Multiscale Modelling of Masonry Structures under Extreme Loading 13/23

14. Mesoscale analysis of large specimens Gattesco, Macorini, Noè(2008) 3D mesoscale model for nonlinear analysis under extreme loading 14/23 Multiscale Modelling of Masonry Structures under Extreme Loading 14/23

15. Partitioning approach: full coupling Communication between parent structure and partitions MPI 15/23 Multiscale Modelling of Masonry Structures under Extreme Loading 15/23

16. Performance of domain partitioning approach mP2P4P8P16P32P64 Partition -2304011530576028801440720 Parent Structure 460803847561500223236724996 Number of nodes for the parent structure and for each partition Monolitic model Model with partitioning Accuracy of the method Domain partitioning approach 16/23 Multiscale Modelling of Masonry Structures under Extreme Loading 16/23

17. Detailed analysis of large structures Domain partitioning approach 162840 nodes – 62 partitions 17/23 Multiscale Modelling of Masonry Structures under Extreme Loading 17/23

18. Partitioning approach: reduced coupling 18/23 Multiscale Modelling of Masonry Structures under Extreme Loading 18/23 Reduced freedoms at parent level via master-slave coupling Reduced freedoms at parent level via master-slave coupling Reduced parent computation and communication Reduced parent computation and communication

19. 19/23 Multiscale Modelling of Masonry Structures under Extreme Loading 19/23 mod1mod2 Effectiveness of reduced coupling

20. 20/23 Multiscale Modelling of Masonry Structures under Extreme Loading 20/23 4 partitions Time FhFh pvpv mod1 58.56 s mod2 40.59 s Elastic analysis Effectiveness of reduced coupling

21. 21/23 Multiscale Modelling of Masonry Structures under Extreme Loading 21/23 4 partitions Time FhFh pvpv mod1 1303.9 s mod2 978.59 s Nonlinear analysis mod1 mod2 Plastic work (interfaces) at peak load Effectiveness of reduced coupling

22. Conclusions Accurate multiscale numerical method for brick- masonry using domain partitioning at structural scale with an accurate model at mesoscale Accurate multiscale numerical method for brick- masonry using domain partitioning at structural scale with an accurate model at mesoscale Effectiveness of developed partitioning method compared to monolithic approach demonstrated by significant speed-up and computational feasibility Effectiveness of developed partitioning method compared to monolithic approach demonstrated by significant speed-up and computational feasibility Developed partitioning method maintains similar accuracy of detailed monolithic mesoscale method even with the reduced coupling approach Developed partitioning method maintains similar accuracy of detailed monolithic mesoscale method even with the reduced coupling approach 22/23 Multiscale Modelling of Masonry Structures under Extreme Loading 22/23

23. Acknowledgements 23/23 Multiscale Modelling of Masonry Structures under Extreme Loading 23/23 7th European Community Framework Programme, Marie Curie Intra-European Fellowship 7th European Community Framework Programme, Marie Curie Intra-European Fellowship High Performance Computing Services, High Performance Computing Services, Imperial College London

24. XI International Conference on COMPUTATIONAL PLASTICITY FUNDAMENTALS AND APPLICATIONS COMPLAS XI 7-9 September 2011 Barcelona - Spain Multiscale Modelling of Masonry Structures under Extreme Loading B A Izzuddin and L Macorini Department of Civil and Environmental Engineering Imperial College London, UK