Multilevel approach for brick masonry walls. I: A numerical strategy for the nonlinear analysis. (English) Zbl 1173.74382

Summary: A numerical strategy based on a multilevel approach is presented for the nonlinear analysis of brick masonry walls as in-plane prototypes of large masonry structures. The strategy is based on an iterative scheme which uses two different, local and global, modelings of the masonry mechanics contemporarily. The former is the reference mechanical model and is defined at the fine scale of the bricks and mortar joints and describes their nonlinear mechanical interaction including damage evolution and friction toughness phenomena. The latter is a linearized Finite Element approximation of the previous model, defined at the rough scale of the wall and used to accelerate the iteration.
The proposed iterative scheme proves to be efficient and robust in both linear and nonlinear contexts.


74Q99 Homogenization, determination of effective properties in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI


[1] Formica, G.; Sansalone, V.; Casciaro, R., A mixed solution strategy for the nonlinear analysis of brick masonry walls, Comput. methods appl. mech. engrg., 191, 51-52, 5847-5876, (2002) · Zbl 1083.74607
[2] Trottenberg, U.; Oosterlee, C.; Schüller, A., Multigrid, (2001), Academic Press London, with guest contributions by Brandt A, Oswald P, Stüben K
[3] Brandt, A., Multi-level adaptive solutions to boundary-value problems, Math. comput., 31, 138, 333-390, (1977) · Zbl 0373.65054
[4] Lopez, S.; Casciaro, R., Algorithmic aspects of adaptive multigrid finite element analysis, Int. J. numer. methods engrg., 40, 919-936, (1997) · Zbl 0886.73068
[5] G. Formica, Multilevel analysis of masonry buildings. Ph.D.Thesis in Computational Mechanics, University of Calabria (Italy), 2005. Available on: <www.labmec.unical.it/pubblicazioni/dottorato.php>.
[6] Uva, G.; Salerno, G., Towards a multiscale analysis of periodic masonry brickwork: a FEM algorithm with damage and friction, () · Zbl 1121.74445
[7] Salerno, G.; Bilotta, A.; Porco, F., A finite element with micro-scale effects for the linear analysis of masonry brickwork, Comput. methods appl. mech. engrg., 190, 4365-4378, (2001)
[8] G. Salerno, G. De Felice, Continuum modeling of discrete systems: a variational approach, in: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS, Barcelona, Spain, 2000.
[9] G.M. Calvi, G. Magenes, Experimental research on response of URM building systems, in: Proceedings of the U.S.-Italy Workshop on Guidelines for Seismic Evaluation and Rehabilitation of Unreinforced Masonry Buildings Pavia, Technical Report NCEER-94-0021, National Centre for Earthquake Engineering, Buffalo, 20 July, 1994.
[10] Gambarotta, L.; Lagomarsino, S., Damage models for the seismic response of brick masonry shear walls. part II: the continuum model and its applications, Earthquake engn. struct. dyn., 26, 441-462, (1997)
[11] Gambarotta, L.; Lagomarsino, S., A microcrack damage model for brittle materials, Int. J. solids struct., 30, 2, 177-198, (1993) · Zbl 0775.73196
[12] Gambarotta, L.; Lagomarsino, S., Damage models for the seismic response of brick masonry shear walls. part I: the mortar joint model and its applications, Earthquake engrg. struct. dyn., 26, 423-439, (1997)
[13] Garcea, G.; Trunfio, A.; Casciaro, R., Mixed formulation and locking in path-following nonlinear analysis, Comput. methods appl. mech. engrg., 165, 247-272, (1998) · Zbl 0954.74061
[14] Riks, E., An incremental approach to the solution of snapping and buckling problems, Int. J. solids struct., 15, 529-551, (1979) · Zbl 0408.73040
[15] Salerno, G.; Casciaro, R., Mode jumping and attractive paths in multimode elastic buckling, Int. J. numer. methods engrg., 40, 833-861, (1997) · Zbl 0886.73019
[16] MUMA code, MUltilevel analysis of MAsonry walls, soon free download on the Italian web site of the Laboratory of Computational Mechanics of the University of Calabria (Italy). Available from: <www.labmec.unical.it>.
[17] S. Brasile, G. Formica, R. Casciaro, 3D Finite Element modelling of panels in boxed and partially framed structures (in Italian), in: Proceedings of the XI ANIDIS National Conference, Genova, Italy, 2004.
[18] Magenes, G.; Calvi, G.M., In-plane seismic response of brick masonry walls, Earthquake engrg. struct. dyn., 26, 109, 1091-1112, (1997)
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