Comptes Rendus
no. 8
Overall ultimate yield strength of a quasi-periodic masonry
[Domaine de résistance macroscopique d'une maçonnerie quasi-périodique]

Présenté par : Jean-Baptiste Leblond

Karam Sab1
1 Université Paris-Est, UR Navier, École des Ponts ParisTech, 6 & 8, avenue Blaise-Pascal, 77455 Marne-la-Vallée cedex 2, France
Comptes Rendus. Mécanique, Volume 337 (2009) no. 8, pp. 603-609.

L'objet de cette Note est la détermination du domaine de résistance homogénéisé dans le plan d'une maçonnerie quasi-périodique constituée de blocs infiniment résistants en contact à travers des interfaces de Mohr–Coulomb sans cohésion. Cette maçonnerie est obtenue en perturbant aléatoirement la dimension horizontale des blocs à partir d'une maçonnerie périodique. On trouve que, dans certains cas non triviaux, le domaine de résistance coincide exactement avec celui de la maçonnerie périodique initiale.

The purpose of this Note is the determination of the in-plane homogenized strength domain of a “quasi-periodic” masonry under the assumption of infinitely resistant blocks connected by cohesionless Mohr–Coulomb interfaces. This masonry is obtained by introducing a random perturbation on the horizontal width of the blocks of a periodic running bond masonry. It is found that in some non-trivial cases the strength domain coincides exactly with that of the initial periodic masonry.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.06.034
Keywords: Solids and structures, Homogenization, Strength domain, Random microstructure, Bounds, Masonry, Mohr–Coulomb
Mot clés : Solides et structures, Homogénéisation, Domaine de résistance, Microstructure aléatoire, Bornes, Maçonnerie, Mohr–Coulomb
Karam Sab 1

1 Université Paris-Est, UR Navier, École des Ponts ParisTech, 6 & 8, avenue Blaise-Pascal, 77455 Marne-la-Vallée cedex 2, France 
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Karam Sab. Overall ultimate yield strength of a quasi-periodic masonry. Comptes Rendus. Mécanique, Volume 337 (2009) no. 8, pp. 603-609. doi : 10.1016/j.crme.2009.06.034. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.06.034/

[1] P. de Buhan; G. de Felice A homogenization approach to the ultimate strength of brick masonry, J. Mech. Phys. Solids, Volume 45 (1997) no. 7, pp. 1085-1104

[2] K. Sab Yield design of thin periodic plates by a homogenization technique and an application to masonry walls, C. R. Mécanique, Volume 331 (2003), pp. 641-646

[3] J. Dallot; K. Sab; O. Godet Experimental validation of a homogenized plate model for the yield design of masonry walls, C. R. Mécanique, Volume 336 (2008), pp. 487-492

[4] F. Cluni; V. Gusella Homogenization of non-periodic masonry structures, Int. J. Solids Struct., Volume 41 (2004) no. 7, pp. 1911-1923

[5] G. Falsone; M. Lombardo Stochastic representation of the mechanical properties of irregular masonry structures, Int. J. Solids Struct., Volume 44 (2007), pp. 8600-8612

[6] A. Cecchi; K. Sab Discrete and continuous models for in plane loaded random elastic brickwork, Eur. J. Mech. A/Solids, Volume 28 (2009) no. 3, pp. 610-625

[7] A. Cecchi; K. Sab A homogenized Love–Kirchhoff model for out-of-plane loaded random 2D lattices. Application to “quasi-periodic” brickwork panels, Int. J. Solids Struct., Volume 46 (2009) no. 14–15, pp. 2907-2919

[8] K. Sab Hill's principle and homogenization of random materials, C. R. Acad. Sci., Sér. II, Volume 312 (1991) no. 1, pp. 1-5

[9] K. Sab Homogenization of non-linear random media by a duality method. Application to plasticity, Asymptotic Anal., Volume 9 (1994), pp. 311-336

[10] K. Sab; A. Cecchi; J. Dallot Determination of the overall yield strength domain of out-of-plane loaded brick masonry, Int. J. Multiscale Comput. Eng., Volume 5 (2007), pp. 83-92

[11] M.I. Idiart; H. Moulinec; P.P. Castaneda; P. Suquet Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations, J. Mech. Phys. Solids, Volume 54 (2006) no. 5, pp. 1029-1063

[12] J. Salençon An introduction to the yield design theory and its application in soil mechanics, Eur. J. Mech. A/Solids, Volume 9 (1990) no. 5, pp. 477-550

[13] G.C. Papanicolaou; S.R.S. Varadhan Boundary value problems with rapidly oscillating random coefficients (J. Fritz; J.L. Lebowitz; D. Szasz, eds.), Random Fields: Rigorous Results in Statistical Mechanics and Quantum Field Theory, Colloquia Mathematica Societatis Janos Bolyai, vol. 2, North Holland, Elsevier Science Publishers, Amsterdam, New York, Oxford, 1979, pp. 835-873

[14] S.M. Kozlov Averaging of random operators, Math. USSR Sb., Volume 37 (1980) no. 2, pp. 167-180

[15] M. Ostoja-Starzewski Material spatial randomness: From statistical to representative volume element, Probab. Eng. Mech., Volume 21 (2006), pp. 112-132

[16] F. Pradel; K. Sab Homogenization of discrete media, J. Phys. IV, Volume 8 (1998) no. P8, pp. 317-324

[17] C. Florence; K. Sab A rigorous homogenization method for the determination of the overall ultimate strength of periodic discrete media and an application to general hexagonal lattices of beams, Eur. J. Mech. A/Solids, Volume 25 (2006) no. 1, pp. 72-97

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