1. The Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing 3-6 September 2013 Cagliari, Sardinia, Italy Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures L. Macorini - B.A. Izzuddin Computational Structural Mechanics Group Department of Civil and Environmental Engineering Imperial College London, UK

2. Outline Advanced modelling for URM Advanced modelling for URM Mesoscale Partitioned Modelling Mesoscale Partitioned Modelling Domain Partitioning approach Domain Partitioning approach 1/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 1/28 3D Mesoscale model 3D Mesoscale model Conclusions Conclusions Enhancements to improve efficiency Enhancements to improve efficiency

3. Mesoscale model Two-material approach Mesoscale scale Advanced modelling for URM 2/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 2/28 (Massart, 2007) Mesoscale descriptions for URM guarantee accurate response prediction Mesoscale descriptions for URM guarantee accurate response prediction Detailed mesoscale models are usually computationally demanding Detailed mesoscale models are usually computationally demanding

4. Mesoscale Partitioned Modelling Structural scale Solid elements and 2D nonlinear interfaces An advanced 3D mesoscale model is combined with partitioning approach Partitioning approach with super-elements for masonry Partitioning approach with super-elements for masonry Parallel computing Parallel computing 3/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 3/28

5. 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 4/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 4/28

6. 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 5/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 5/28

7. 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 6/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 6/28

8. In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) Wpl1 Wpl2 7/28 Nonlinear Analysis of Masonry Structures using Mesoscale Partitioned Modelling 7/28 3D mesoscale model for nonlinear analysis under extreme loading

9. Out-of-plane behaviour Chee Liang, N.G. (1996) Wpl1Wpl1Wpl1 8/28 Nonlinear Analysis of Masonry Structures using Mesoscale Partitioned Modelling 8/28 3D mesoscale model for nonlinear analysis under extreme loading

10. Mesoscale analysis of large URM components Gattesco et al. (2008) 3D mesoscale model for nonlinear analysis under extreme loading 9/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 9/28

11. Mesoscale analysis to represent quasi-brittle behaviour A) B) Dynamic analyses with a large number of time steps are used for representing post-peak response Dynamic analyses with a large number of time steps are used for representing post-peak response 3D mesoscale model for nonlinear analysis under extreme loading 10/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 10/28

12. Domain partitioning approach 11/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 11/28

13. Domain partitioning approach Communication between parent structure and partitions MPI 12/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 12/28

14. Detailed analysis of large structures Domain partitioning approach 162840 nodes – 62 partitions  m [MPa] W pl1m [MPa] 13/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 13/28

15. Detailed analysis of large structures Domain partitioning approach 14/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 14/28 When analysing large URM structures, the most critical process becomes that of the parent structure. This may significantly reduce efficiency leading to an excessively long wall-clock time. When analysing large URM structures, the most critical process becomes that of the parent structure. This may significantly reduce efficiency leading to an excessively long wall-clock time. 162840 nodes 62 partitions 62 partitions

16. Detailed analysis of large structures Domain partitioning approach 15/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 15/28 Enhancements to improve efficiency: Enhancements to improve efficiency: - Hierarchic partitioning - Hierarchic partitioning - Mixed-dimensional coupling - Mixed-dimensional coupling 162840 nodes 62 partitions 62 partitions

17. Enhancements to improve efficiency Enhanced domain partitioning approach Modelling with hierarchic partitioning (Jokhio 2012)Modelling with hierarchic partitioning (Jokhio 2012) 16/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 16/28

18. Enhancements to improve efficiency Enhanced domain partitioning approach Modelling with partitions and master-slave coupling (Jokhio 2012)Modelling with partitions and master-slave coupling (Jokhio 2012) 6 DoF Mixed-dimensional coupling 17/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 17/28

19. Enhancements to improve efficiency Enhanced domain partitioning approach Modelling heterogeneous structures with URMModelling heterogeneous structures with URM Infilled frame 18/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 18/28 Elasto-plastic beam elements are used for modelling beams and columns of the frame, while the detailed mesoscale description is utilised for URM panels

20. Numerical examples Enhanced domain partitioning approach Numerical performance (Speed-up)Numerical performance (Speed-up) Elastic analysis of a large URM wall (48  48 20-noded solid elements) Prescribed top vertical displacements in 1 step and top horizontal displacements in 10 steps 19/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 19/28 uzuz uxux

21. Numerical examples Enhanced domain partitioning approach Numerical performance (Speed-up)Numerical performance (Speed-up) Elastic analysis of a large URM wall (48  48 20-noded solid elements) Standard (flat) Partitioning Approach Enhanced Partitioning Approach (hierarchic partitioning) P-L1 P-L2 20/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 20/28

22. Numerical examples Enhanced domain partitioning approach Numerical performance – Speed-upNumerical performance – Speed-up Elastic analysis of a large URM wall (48  48 20-noded solid elements) model N. processors Parent Struct. DOFs Part. L1 DOFs Part. L2 DOFs S m1142848--- P452304 36864 -4.60 P16176912 9792 -6.96 P646516128 2736 -3.24 P4 mslc5576 36864 -3.73 P16 mslc171728 9792 -12.43 P64 mslc654032 2736 -116.39 P4  4 207682304979214.40 P4  16 69 76823042736 28.65 P4  4 mslc 2096576979217.63 P4x16 mslc69965762736205.50 S i = T m /T Si T m = 13152 s 21/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 21/28 flat partitioning

23. Numerical examples Enhanced domain partitioning approach Numerical performance – Speed-upNumerical performance – Speed-up Elastic analysis of a large URM wall (48  48 20-noded solid elements) 22/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 22/28 S i = T m /T Si T m = 13152 s Flat partitioning

24. Numerical examples Enhanced domain partitioning approach Numerical performance – Speed-upNumerical performance – Speed-up Elastic analysis of a large URM wall (48  48 20-noded solid elements) model N. processors Parent Struct. DOFs Part. L1 DOFs Part. L2 DOFs S m1142848--- P452304 36864 -4.60 P16176912 9792 -6.96 P646516128 2736 -3.24 P4 mslc5576 36864 -3.73 P16 mslc171728 9792 -12.43 P64 mslc654032 2736 -116.39 P4  4 207682304979214.40 P4  16 69 76823042736 28.65 P4  4 mslc 2096576979217.63 P4x16 mslc69965762736205.50 S i = T m /T Si T m = 13152 s 21/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 21/28 flat partitioning with mixed-dimensional coupling hierarchic partitioning hierarchic partitioning with mixed-dimensional coupling

25. Enhancements to improve efficiency Enhanced domain partitioning approach Numerical performance – Speed-upNumerical performance – Speed-up Elastic analysis of a large URM wall (48  48 20-noded solid elements) S i = T m /T Si T m = 13152 s 23/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 23/28

26. Enhancements to improve efficiency Enhanced domain partitioning approach Solution accuracy: partitioned vs. monolithic modelSolution accuracy: partitioned vs. monolithic model Normal stresses after the application of the vertical displacement 24/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 24/28

27. Enhancements to improve efficiency Enhanced domain partitioning approach Solution accuracy: partitioned vs. monolithic modelSolution accuracy: partitioned vs. monolithic model Normal stresses at the end of the analysis 24/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 24/28

28. Numerical examples Enhanced domain partitioning approach Analysis of heterogeneous structures under extreme loadingAnalysis of heterogeneous structures under extreme loading 25/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 25/28

29. Numerical examples 26/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 26/28 Enhanced domain partitioning approach Analysis of heterogeneous structures under extreme loadingAnalysis of heterogeneous structures under extreme loading Blast pressure in time Model validation under blast loading (Macorini and Izzuddin 2013)

30. Numerical examples Enhanced domain partitioning approach 27/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 27/28 Analysis of heterogeneous structures under extreme loadingAnalysis of heterogeneous structures under extreme loading

31. Conclusions 28/28 Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures 28/28 When using hierarchic partitioning and master-slave coupling, contrary to the case of flat partitioning, computational efficiency is preserved also in the analysis of URM structures modelled using a large number of partitions When using hierarchic partitioning and master-slave coupling, contrary to the case of flat partitioning, computational efficiency is preserved also in the analysis of URM structures modelled using a large number of partitions In the case of master-slave coupling the gain in computational performance is obtained losing accuracy depending upon the specific loading conditions In the case of master-slave coupling the gain in computational performance is obtained losing accuracy depending upon the specific loading conditions This limitation will be overcome in next enhancements by introducing soft coupling using a Lagrangian multiplier approach This limitation will be overcome in next enhancements by introducing soft coupling using a Lagrangian multiplier approach

32. Acknowledgements The authors gratefully acknowledge the High Performance Computing (HPC) Services at Imperial College London for providing and supporting the required computing facilities. Enhanced Mesoscale Partitioned Modelling for Unreinforced Masonry Structures