Keywords: masonry, numerical modelling, multisurface plasticity, displacement discontinuities.

Masonry is one of the most ancient structural materials. It can be seen as a composite material composed of solid elements (stone, brickwork) tied together by mortar joints. Each component has its influence on the behaviour of the assembly as well as the bond conditions. In recent years, with the increasing complexity of masonry structures and the increasing requirement to better assess the strength of existing masonry structures and to improve their design, there is a need for introducing the computer modelling of such structures. The principal difficulty in that endeavor is to elaborate robust and reliable models to determine how masonry structure reacts to extreme conditions with a non linear behaviour. A number of authors have studied this problem and proposed different approaches depending on the level of refinement given to the description of the geometry [1,2].

The identification of the local failure mechanisms and previous works show the importance of bricks crushing modes in order to build a sufficiently predictive model. Moreover, it is well known that such materials exhibit softening behaviour and produce mesh sensitivity of the model. Usually, we find (e.g. [1]) approaches in which softening behaviour is condensed in mortar joints and not in units.

Our approach consists in taking into account the two materials employing continuous model, and integrate bricks crushing failure mechanisms in units. These mechanisms are represented with strong displacement discontinuities within the framework of incompatible mode method, solving the problem of mesh sensitivity.

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Units modelling: Non linear softening behaviour of such material is captured with strong displacement discontinuities within the framework of incompatible mode method [3,4]. Actually, two fixed-orientation discontinuities have been implemented. The vertical mode concerns bricks cracking in tension. The second horizontal mode, represents bricks crushing under compression.

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Joints modelling: Non linear behaviour of this zone is associated with two phenomena which are mode I tension opening and mode II frictional sliding. The latter is moreover influenced by dilatancy which consists in the uplift of one unit over the other. Constitutive model was here developed within the plasticity theory framework according to this phenomenological approach. This approach is well established and leads to robust algorithms [5]. In this work, elastic domain is bounded by a multisurface yield criterion which consists in a Drucker-Prager criterion for mode II joints slipping and a tension cut-off for mode I joints opening.

This model has been implemented in the finite element code FEAP [6] and compared with results obtained by two experimental campaigns made on masonry shear walls (see [7,8]). We show it leads to good predictive results considering the case of walls built up with hollow bricks and to reasonable results considering small solid bricks walls. Such result is coherent with the presented model main hypothesis concerning the importance of brick crushing mechanisms.

1

P.B. Lourenço and J.G. Rots. Multisurface interface model for analysis of masonry structures. Journal of engineering mechanics, 123(7):660-668, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:7(660)

2

J. Lopez, S. Oller, and J. Lubliner. A homogeneous constitutive model for masonry. International journal for numerical methods in engineering, 46(10), 1999. doi:10.1002/(SICI)1097-0207(19991210)46:10<1651::AID-NME718>3.0.CO;2-2

3

A. Ibrahimbegovic and E.L. Wilson. A modified method of incompatible modes. Communication in Numerical Methods and Engineering, 7:187-194, 1991. doi:10.1002/cnm.1630070303

4

D. Brancherie, A. Delaplace, and A. Ibrahimbegovic. Formulation and finite element implementation of continuum / discrete strain softening models. In Fifth World Congress on Computational Mechanics (WCCM V), pages 781-784, Vienna, Austria, July 7-12, 2002. Editors: Mang, H.A.; Rammerstorfer, F.G.; Eberhardsteiner, J.

5

J.C. Simo and T.J.R. Hughes. Computational Inelasticity. Springer, New York, 1998.

6

O.C. Zienkiewicz and R.L. Taylor. The Finite Element Method: Basic Formulation and Linear Problems. McGraw-Hill, London, 1989.

7

P.B. Lourenço. Computational strategies for masonry structures. PhD thesis, Delft University of Technology, 1996.

8

B. Capra, J.I. Cruz-Diaz, P. Delmotte, A. Mebarki, P. Rivillon, and A. Sellier.
Murs de contreventement en maçonneries de terre cuite. Cahiers du CSTB, (3310), 2001.

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