Cauchy and Cosserat Equivalent Continua for the Multiscale Analysis of Periodic Masonry Walls

  • Daniela Addessi
  • Elio Sacco
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 58)


The present paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. Masonry is considered a composite material obtained as a regular distribution of blocks connected by horizontal and vertical mortar joints. The macromechanical equivalent Cauchy and Cosserat models are derived by means of the homogenization procedure, which make use of the Transformation Field Analysis (FTA) in order to account for the nonlinear effects occurring in the components. The micromechanical analysis is developed considering a Cauchy model for the masonry components. In particular, the linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is proposed for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Numerical applications are performed in order to assess the performances of the proposed models in reproducing the mechanical behavior of the masonry material. In particular, two different masonry textures are considered, remarking their different behavior.Moreover, for one masonry texture, the response is derived considering two possible RVEs.


Representative Volume Element Inelastic Strain Masonry Wall Mortar Joint Cosserat Continuum 
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  1. 1.
    Luciano, R., Sacco, E.: Homogenization technique and damage model for old masonry material. International Journal of Solids and Structures 34(24), 3191–3208 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Massart, T.J., Peerlings, R.H.J., Geers, M.G.D.: An enhanced multi-scale approach for masonry wall computations with localization of damage. International Journal on Numerical Methods in Engineering 69(5), 1022–1059 (2007)zbMATHCrossRefGoogle Scholar
  3. 3.
    Brasile, S., Casciaro, R., Formica, G.: Multilevel approach for brick masonry walls. Part I: A numerical strategy for the nonlinear analysis. Computer Methods in Applied Mechanics and Engineering 196, 4934–4951 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kouznetsova, V., Geers, M.G.D., Brekelmans, W.A.M.: Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. International Journal on Numerical Methods in Engineering 54, 1235–1260 (2002)zbMATHCrossRefGoogle Scholar
  5. 5.
    Forest, S., Sab, K.: Cosserat overall modeling of heterogeneous materials. Mechanics Research Communications 25, 449–454 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Van der Sluis, O., Vosbeek, P.H.J., Schreurs, P.J.G., Meijer, H.E.H.: Homogenization of heterogeneous polymers. International Journal of Solids and Structures 36, 3193–3214 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Trovalusci, P., Masiani, R.: Non-linear micropolar and classical continua for anisotropic discontinuous materials. International Journal of Solids and Structures 40(5), 1281–1297 (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Dvorak, G.J.: Transformation field analysis of inelastic composite materials. Proc. Roy. Soc. London A 437, 311–327 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Michel, J.C., Suquet, P.: Nonuniform transformation field analysis. International Journal of Solids and Structures 40, 6937–6955 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Sacco, E.: A nonlinear homogenization procedure for periodic masonry. European Journal of Mechanics A, Solids 28, 209–222 (2009)zbMATHCrossRefGoogle Scholar
  11. 11.
    Addessi, D., Sacco, E., Paolone, A.: Cosserat model for periodic masonry deduced by nonlinear homogenization. European Journal of Mechanics A, Solids 39, 724–737 (2010)CrossRefGoogle Scholar
  12. 12.
    Anthoine, A.: Homogenization of periodic masonry: Plane stress, generalized plane strain or 3D modelling? Communications in Numerical Methods in Engineering 13, 319–326 (1997)zbMATHCrossRefGoogle Scholar
  13. 13.
    Hill, R.: Theory of mechanical properties of fibre-strengthened materials: II. Inelastic behaviour. Journal of the Mechanics and Physics of Solids 12, 213–218 (1964)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Mandel, J.: Plasticité Classique et Viscoplasticité. CISM Lecture Notes. Springer, Heidelberg (1971)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Daniela Addessi
    • 1
  • Elio Sacco
    • 2
  1. 1.Department of Structural EngineeringUniversity of Rome “Sapienza”RomeItaly
  2. 2.Department of Mechanics, Structures and EnvironmentUniversity of CassinoCassinoItaly

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