Mesoscopic modelling of masonry using weak and strong discontinuities. (English) Zbl 1297.74100

Summary: A mesoscopic masonry model is presented in which joints are modelled by weak and strong discontinuities through the partition of unity property of finite element shape functions. A Drucker-Prager damage model describes joint degradation whereas the bricks remain linear elastic throughout the simulations. Analogies and differences amongst strong and weak discontinuity models are discussed, with special emphasis on kinematic description and implementation. Mesh sensitivity and performance of the presented models are illustrated by two-brick, three-point bending and shear wall tests.


74P15 Topological methods for optimization problems in solid mechanics
74P10 Optimization of other properties in solid mechanics
74A45 Theories of fracture and damage
Full Text: DOI


[1] Lourenço, P. B.; Rots, J. G.; Blaauwendraad, J., Two approaches for the analysis of masonry structures, HERON, 40, 4, 313-340, (1995)
[2] J.G. Rots, Structural masonry: an experimental/numerical basis for practical design rules (CUR report 171), Technical report, Civieltechnisch Centrum Uitvoering Research en Regelgeving, 1997.
[3] A. Orduña, P.B. Lourenco, Limit analysis as a tool for the simplified assessment of ancient masonry structures, in: Proceedings of the Historical Constructions 2001, 2001, pp. 511-520.
[4] Rots, J. G.; Blaauwendraad, J., Crack models for concrete: discrete or smeared? fixed, multi-directional or rotating?, HERON, 34, 1, 1-59, (1989)
[5] Wells, G. N.; Sluys, L. J., On the conceptual equivalence of embedded strong discontinuity and smeared crack formulations, HERON, 46, 3, 181-189, (2001)
[6] Alfaiate, J. V.; Simone, A.; Sluys, L. J., Non-homogeneous displacement jumps in strong embedded discontinuities, Int. J. Solids Struct., 40, 21, 5799-5817, (2003) · Zbl 1059.74548
[7] Sluys, L. J.; Cauvern, M.; De Borst, R., Discretization influence in strain-softening problems, Engrg. Comput., 12, 3, 209-228, (1995) · Zbl 0824.73080
[8] Jirásek, M.; Bažant, Z. P., Inelastic analysis of structures, (2002), John Wiley & Sons, Ltd. Chichester
[9] Pijaudier-Cabot, G.; Bažant, Z. P., Non-local damage theory, ASCE J. Engrg. Mech., 113, 10, 1512-1533, (1987)
[10] Needleman, A., Material rate dependence and mesh sensitivity in localization problems, Comput. Methods Appl. Mech. Engrg., 67, 1, 69-85, (1988) · Zbl 0618.73054
[11] de Borst, R.; Sluys, L. J., Localization in a Cosserat continuum under static and dynamic loading conditions, Comput. Methods Appl. Mech. Engrg., 90, 1-3, 805-827, (1991)
[12] Sluys, L. J.; de Borst, R., Wave-propagation and localization in a rate-dependent cracked medium model formulation and one-dimensional examples, Int. J. Solids Struct., 29, 23, 2945-2958, (1992)
[13] Peerlings, R. H.J.; de Borst, R.; Brekelmans, W. A.M.; Geers, M. G.D., Gradient-enhanced damage modelling of concrete fracture, Mech. Cohes. Frict. Mater., 3, 4, 323-342, (1998) · Zbl 0938.74006
[14] Jirásek, M., Nonlocal damage mechanics, Damage Fract. Geomater., 11, 993-1021, (2007)
[15] Belytschko, T.; Fish, J.; Engelmann, B. E., A finite-element with embedded localization zones, Comput. Methods Appl. Mech. Engrg., 70, 1, 59-89, (1988) · Zbl 0653.73032
[16] Sluys, L. J.; Berends, A. H., Discontinuous failure analysis for mode-I and mode-II localization problems, Int. J. Solids Struct., 35, 31-32, 4257-4274, (1998) · Zbl 0933.74060
[17] Huespe, A. E.; Needleman, A.; Oliver, J.; Sanchez, P. J., A finite thickness band method for ductile fracture analysis, Int. J. Plast., 25, 12, 2349-2365, (2009)
[18] Oliver, J.; Cervera, M.; Manzoli, O., Strong discontinuities and continuum plasticity models: the strong discontinuity approach, Int. J. Plast., 15, 3, 319-351, (1999) · Zbl 1057.74512
[19] De Proft, K.; Wells, G. N.; Sluys, L. J.; De Wilde, W. P., An experimental-computational investigation of fracture in brittle materials, Comput. Concr., 1, 3, 227-248, (2004)
[20] Simone, A.; Duarte, C. A.; Van der Giessen, E., A generalized finite element method for polycrystals with discontinuous grain boundaries, Int. J. Numer. Methods Engrg., 67, 8, 1122-1145, (2006) · Zbl 1113.74076
[21] Schellekens, J. C.J.; de Borst, R., On the numerical integration of interface elements, Int. J. Numer. Methods Engrg., 36, 1, 43-66, (1993) · Zbl 0825.73840
[22] Swenson, D. V.; Ingraffea, A. R., Modeling mixed-mode dynamic crack propagation using finite elements: theory and applications, Comput. Mech., 3, 381-397, (1988) · Zbl 0663.73074
[23] Simo, J. C.; Oliver, J.; Armero, F., An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Comput. Mech., 12, 227-296, (1993) · Zbl 0783.73024
[24] Jirásek, M., Comparative study on finite elements with embedded discontinuities, Comput. Methods Appl. Mech. Engrg., 188, 1-3, 307-330, (2000) · Zbl 1166.74427
[25] Babuska, I.; Melenk, J. M., The partition of unity method, Int. J. Numer. Methods Engrg., 40, 4, 727-758, (1997) · Zbl 0949.65117
[26] Lourenço, P. B.; De Borst, R.; Rots, J. G., A plane stress softening plasticity model for orthotropic materials, Int. J. Numer. Methods Engrg., 40, 21, 4033-4057, (1997) · Zbl 0897.73015
[27] Zucchini, A.; Lourenço, P. B., A micro-mechanical model for the homogenisation of masonry, Int. J. Solids Struct., 39, 12, 3233-3255, (2002) · Zbl 1049.74754
[28] Milani, G., Simple homogenization model for the non-linear analysis of in-plane loaded masonry walls, Comput. Struct., 89, 17-18, 1586-1601, (2011)
[29] 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, 4, 423-439, (1997)
[30] Lourenço, P. B.; Rots, J. G., Multisurface interface model for analysis of masonry structures, ASCE J. Engrg. Mech., 123, 7, 660-668, (1997)
[31] Giambanco, G.; Rizzo, S.; Spallino, R., Numerical analysis of masonry structures via interface models, Comput. Methods Appl. Mech. Engrg., 190, 49-50, 6493-6511, (2001) · Zbl 1116.74341
[32] Alfaiate, J. V.; de Almeida, J. R., Modelling discrete cracking on masonry walls, Masonry Int., 17, 2, 83-93, (2004)
[33] Oliveira, D. V.; Lourenço, P. B., Implementation and validation of a constitutive model for the cyclic behaviour of interface elements, Comput. Struct., 82, 17-19, 1451-1461, (2004)
[34] Alfano, G.; Sacco, E., Combining interface damage and friction in a cohesive-zone model, Int. J. Numer. Methods Engrg., 68, 5, 542-582, (2006) · Zbl 1275.74021
[35] Senthivel, R.; Lourenço, P. B., Finite element modelling of deformation characteristics of historical stone masonry shear walls, Engrg. Struct., 31, 9, 1930-1943, (2009)
[36] De Proft, K.; Heyens, K.; Sluys, L. J., Mesoscopic modelling of masonry failure, Proc. ICE Engrg. Comput. Mech., 164, EM1, 41-46, (2010)
[37] Dolatshahi, K. M.; Aref, A. J., Two-dimensional computational framework of meso-scale rigid and line interface elements for masonry structures, Engrg. Struct., 33, 12, 3657-3667, (2011)
[38] Brasile, S.; Casciaro, R.; Formica, G., Multilevel approach for brick masonry walls. part I: A numerical strategy for the nonlinear analysis, Comput. Methods Appl. Mech. Engrg., 196, 49-52, 4934-4951, (2007) · Zbl 1173.74382
[39] Massart, T. J.; Peerlings, R. H.J.; Geers, M. G.D., An enhanced multi-scale approach for masonry wall computations with localization of damage, Int. J. Numer. Methods Engrg., 69, 5, 1022-1059, (2007) · Zbl 1194.74283
[40] Addessi, D.; Sacco, E., A multi-scale enriched model for the analysis of masonry panels, Int. J. Solids Struct., 49, 6, 865-880, (2012)
[41] Marfia, S.; Sacco, E., Multiscale damage contact – friction model for periodic masonry walls, Comput. Methods Appl. Mech. Engrg., 205-208, 189-203, (2012) · Zbl 1239.74007
[42] Benvenuti, E.; Tralli, A.; Ventura, G., A regularized XFEM model for the transition from continuous to discontinuous displacements, Int. J. Numer. Methods Engrg., 74, 6, 911-944, (2008) · Zbl 1158.74479
[43] Bathe, K. J., Finite element procedures, (1996), Prentice-Hall · Zbl 0511.73065
[44] Duarte, C. A.M.; Oden, J. T., An hp adaptive method using clouds, Comput. Methods Appl. Mech. Engrg., 139, 237-262, (1996) · Zbl 0918.73328
[45] Simone, A., Partition of unity-based discontinuous elements for interface phenomena: computational issues, Commun. Numer. Methods Engrg., 20, 6, 465-478, (2004) · Zbl 1058.74082
[46] T.M.J. Raijkmakers, A.T. Vermeltvoort, Deformation controlled tests in masonry shear walls - Report B-92-1156, Technical report, TNO Bouw, 1992.
[47] P.H. Feenstra, Implementing an isotropic damage model in Diana. Use-case for the user-supplied subroutine usrmat, in: Proceedings of the Third DIANA World Conference, 2002, pp. 89-97.
[48] Massart, T. J.; Peerlings, R. H.J.; Geers, M. G.D., Mesoscopic modeling of failure and damage-induced anisotropy in brick masonry, Eur. J. Mech. A Solids, 23, 5, 719-735, (2004) · Zbl 1058.74627
[49] Chaimoon, K.; Attard, M. M., Experimental and numerical investigation of masonry under three-point bending (in-plane), Engrg. Struct., 31, 1, 103-112, (2009)
[50] Gutiérrez, M. A., Energy release control for numerical simulations of failure in quasi-brittle solids, Int. J. Numer. Methods Engrg., 20, 1, 19-29, (2004) · Zbl 1047.74551
[51] B. Vandoren, K. De Proft, A. Simone, L.J. Sluys, Modelling crack initiation and propagation in masonry using the partition of unity method, in: The Proceeding of the Eighth International Conference on Fracture Mechanics of Concrete and Concrete Structures, 2013.
[52] Ali, S.; Moore, I. D.; Page, A. W., Substructuring technique in nonlinear analysis of brick masonry subjected to concentrated load, Comput. Struct., 27, 3, 417-425, (1987) · Zbl 0624.73083
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.