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A computational homogenization approach for the study of localization of masonry structures using the XFEM

  • Georgios A. Drosopoulos
  • Georgios E. Stavroulakis
Original
  • 32 Downloads

Abstract

A computational homogenization method is presented in this article, for the investigation of localization phenomena arising in periodic masonry structures. The damage of the macroscopic, structural scale is represented by cohesive cracks, simulated by the extended finite element method. The cohesive traction–separation law along these cracks is built numerically, using a mesoscopic, fine scale, masonry model discretized by classical finite elements. It consists of stone blocks and the mortar joints, simulated by unilateral contact interfaces crossing the boundaries of the mesoscopic structure, assigned a tensile traction–separation softening law. The anisotropic damage induced by the mortar joints can be depicted by this method. In addition, the non-penetration condition between the stone blocks is incorporated in the averaging relations. Sophisticated damage patterns, depicted by several continuous macro-cracks in the masonry structure, can also be represented by the proposed approach. Finally, results are compared well with experimental investigation published in the literature.

Keywords

Masonry Localization XFEM Homogenization Multi-scale Unilateral contact 

Notes

References

  1. 1.
    Tsalis, D., Baxevanis, T., Chatzigeorgiou, G., Charalambakis, N.: Homogenization of elastoplastic composites with generalized periodicity in the microstructure. Int. J. Plast. 51, 161–187 (2013)CrossRefGoogle Scholar
  2. 2.
    Chatzigeorgiou, G., Charalambakis, N., Chemiski, Y., Meraghni, F.: Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials. Int. J. Plast. 81, 18–39 (2016)CrossRefGoogle Scholar
  3. 3.
    Suquet, P.M.: Local and Global Aspects in the Mathematical Theory of Plasticity, Plasticity Today: Modelling, Methods and Applications. Elsevier, London (1985)zbMATHGoogle Scholar
  4. 4.
    Smit, R., Brekelmans, W., Meijer, H.: Prediction of the mechanical behaviour of non-linear heterogeneous systems by multi-level finite element modeling. Comput. Methods Appl. Mech. Eng. 155, 181–192 (1998)CrossRefzbMATHGoogle Scholar
  5. 5.
    Feyel, F.: Multiscale FE\(^2\) elastoviscoplastic analysis of composite structures. Comput. Mater. Sci. 16, 344–354 (1999)CrossRefGoogle Scholar
  6. 6.
    Miehe, C., Schröder, J., Schotte, J.: Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput. Methods Appl. Mech. Eng. 171, 387–418 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kouznetsova, V.: Computational Homogenization for the Multi-scale Analysis of Multi-phase Materials. Ph.D. thesis, Technical University Eindhoven, The Netherlands (2002)Google Scholar
  8. 8.
    Miehe, C., Koch, A.: Computational micro-to-macro transitions of discretized microstructures undergoing small strains. Arch. Appl. Mech. 72, 300–317 (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Borst, R.D., Sluys, L., Muhlhaus, H., Pamin, J.: Fundamental issues in finite element analyses of localization of deformation. Eng. Comput. 10, 99–121 (1993)CrossRefGoogle Scholar
  10. 10.
    Coenen, E.W.C., Kouznetsova, V.G., Geers, M.G.D.: Novel boundary conditions for strain localization analyses in microstructural volume elements. Int. J. Numer. Methods Eng. 90, 1–21 (2012a)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Coenen, E.W.C., Kouznetsova, V.G., Bosco, E., Geers, M.G.D.: A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework. Int. J. Fract. 178, 157–178 (2012b)CrossRefGoogle Scholar
  12. 12.
    Coenen, E.W.C., Kouznetsova, V.G., Geers, M.G.D.: Multi-scale continuous–discontinuous framework for computational homogenization–localization. J. Mech. Phys. Solids 60, 1486–1507 (2012c)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Bosco, E., Kouznetsova, V.G., Geers, M.G.D.: Multi-scale computational homogenization–localization for propagating discontinuities using x-fem. Int. J. Numer. Methods Eng. 102, 496–527 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Belytschko, T., Loehnert, S., Song, J.H.: Multiscale aggregating discontinuities: a method for circumventing loss of material stability. Int. J. Numer. Methods Eng. 73, 869–894 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Belytschko, T., Song, J.H.: Coarse-graining of multiscale crack propagation. Int. J. Numer. Methods Eng. 81, 537–563 (2010)zbMATHGoogle Scholar
  16. 16.
    Souza, F.V., Allen, D.H.: Modeling the transition of microcracks into macrocracks in heterogeneous viscoelastic media using a two-way coupled multiscale model. Int. J. Solids Struct. 48, 3160–3175 (2011)CrossRefGoogle Scholar
  17. 17.
    Huang, T., Zhang, Y., Yang, C.: Multiscale modelling of multiple-cracking tensile fracture behaviour of engineered cementitious composites. Eng. Fract. Mech. 160, 52–66 (2016)CrossRefGoogle Scholar
  18. 18.
    Rabczuk, T., Belytschko, T.: Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int. J. Numer. Methods Eng. 61, 2316–2343 (2004)CrossRefzbMATHGoogle Scholar
  19. 19.
    Rabczuk, T., Zi, G., Bordas, S., Nguyen-Xuan, H.: A simple and robust three-dimensional cracking-particle method without enrichment. Comput. Methods Appl. Mech. Eng. 199, 2437–2455 (2010)CrossRefzbMATHGoogle Scholar
  20. 20.
    Areias, P., Msekh, M., Rabczuk, T.: Damage and fracture algorithm using the screened poisson equation and local remeshing. Eng. Fract. Mech. 158, 116–143 (2016)CrossRefGoogle Scholar
  21. 21.
    Areias, P., Rabczuk, T., da Costa, D.D.: Element-wise fracture algorithm based on rotation of edges. Eng. Fract. Mech. 110, 113–137 (2013)CrossRefGoogle Scholar
  22. 22.
    Talebi, H., Silani, M., Bordas, S.P.A., Kerfriden, P., Rabczuk, T.: A computational library for multiscale modeling of material failure. Comput. Mech. 53, 1047–1071 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Talebi, H., Silani, M., Rabczuk, T.: Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Adv. Eng. Softw. 80, 82–92 (2015)CrossRefGoogle Scholar
  24. 24.
    Budarapu, P.R., Gracie, R., Yang, S.W., Zhuang, X., Rabczuk, T.: Efficient coarse graining in multiscale modeling of fracture. Theor. Appl. Fract. Mech. 69, 126–143 (2014)CrossRefGoogle Scholar
  25. 25.
    Verhoosel, C.V., Remmers, J.J.C., Gutiérrez, M.A., de Borst, R.: Computational homogenization for adhesive and cohesive failure in quasi-brittle solids. Int. J. Numer. Methods Eng. 83, 1155–1179 (2010)CrossRefzbMATHGoogle Scholar
  26. 26.
    Nguyen, V.P., Lloberas-Valls, O., Stroeven, M., Sluys, L.J.: Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks. Comput. Methods Appl. Mech. Eng. 200, 1220–1236 (2011)CrossRefzbMATHGoogle Scholar
  27. 27.
    Nguyen, V.P., Stroeven, M., Sluys, L.J.: An enhanced continuous–discontinuous multiscale method for modelling mode-I failure in random heterogeneous quasibrittle materials. Eng. Fract. Mech. 79, 78–102 (2012a)CrossRefGoogle Scholar
  28. 28.
    Nguyen, V.P., Lloberas-Valls, O., Stroeven, M., Sluys, L.J.: Computational homogenization for multiscale crack modeling. Implementational and computational aspects. Int. J. Numer. Methods Eng. 89, 192–226 (2012b)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Anthoine, A.: Derivation of the in-plane elastic characteristics of masonry through homogenization theory. Int. J. Solids Struct. 32, 137–163 (1995)CrossRefzbMATHGoogle Scholar
  30. 30.
    Luciano, R., Sacco, E.: A damage model for masonry structures. Eur. J. Mech. A Solids 17, 285–303 (1998)CrossRefzbMATHGoogle Scholar
  31. 31.
    Lourenço, P.B.: Anisotropic softening model for masonry plates and shells. J. Struct. Eng. (ASCE) 126, 1008–1016 (2000)CrossRefGoogle Scholar
  32. 32.
    Sacco, E.: A nonlinear homogenization procedure for periodic masonry. Eur. J. Mech. A Solids 28, 209–222 (2009)CrossRefzbMATHGoogle Scholar
  33. 33.
    Casolo, S., Milani, G.: A simplified homogenization-discrete element model for the non-linear static analysis of masonry walls out-of-plane loaded. Eng. Struct. 32, 2352–2366 (2010)CrossRefGoogle Scholar
  34. 34.
    Milani, G.: Simple lower bound limit analysis homogenization model for in- and out-of-plane loaded masonry walls. Constr. Build. Mater. 25, 4426–4443 (2011)CrossRefGoogle Scholar
  35. 35.
    Milani, G., Pizzolato, M., Tralli, A.: Simple numerical model with second order effects for out-of-plane loaded masonry walls. Eng. Struct. 48, 98–120 (2013a)CrossRefGoogle Scholar
  36. 36.
    Milani, G., Esquivel, Y.W., Lourenço, P.B., Riveiro, B., Oliveira, D.V.: Characterization of the response of quasi-periodic masonry: geometrical investigation, homogenization and application to the Guimares castle, Portugal. Eng. Struct. 56, 621–641 (2013b)CrossRefGoogle Scholar
  37. 37.
    Massart, T.J., Peerlings, R.H.J., Geers, M.G.D.: Structural damage analysis of masonry walls using computational homogenization. Int. J. Damage Mech. 16, 199–226 (2007a)CrossRefGoogle Scholar
  38. 38.
    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 Eng. 69, 1022–1059 (2007b)CrossRefzbMATHGoogle Scholar
  39. 39.
    Mercatoris, B., Bouillard, P., Massart, T.: Multi-scale detection of failure in planar masonry thin shells using computational homogenisation. Eng. Fract. Mech. 76, 479–499 (2009)CrossRefGoogle Scholar
  40. 40.
    Mercatoris, B., Massart, T.: A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry. Int. J. Numer. Methods Eng. 85, 1177–1206 (2011)CrossRefzbMATHGoogle Scholar
  41. 41.
    Petracca, M., Pelà, L., Rossia, R., Ollera, S., Camatac, G., Spaconec, E.: Multiscale computational first order homogenization of thick shells for the analysis of out-of-plane loaded masonry walls. Comput. Methods Appl. Mech. Eng. 315, 273–301 (2017)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Drosopoulos, G.A., Wriggers, P., Stavroulakis, G.E.: A multi-scale computational method including contact for the analysis of damage in composite materials. Comput. Mater. Sci. 95, 522–535 (2014)CrossRefGoogle Scholar
  43. 43.
    Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131–150 (1999)CrossRefzbMATHGoogle Scholar
  44. 44.
    Moës, N., Belytschko, T.: Extended finite element method for cohesive crack growth. Eng. Fract. Mech. 69, 813–833 (2002)CrossRefGoogle Scholar
  45. 45.
    Bordas, S., Nguyen, P.V., Duvant, C., Guidoum, A., Nguyen-Dang, H.: An extended finite element library. Int. J. Numer. Methods Eng. 71, 703–732 (2007)CrossRefzbMATHGoogle Scholar
  46. 46.
    Natarajan, S., Bordas, S., Mahapatra, D.R.: Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping. Int. J. Numer. Methods Eng. 80, 103–134 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Khoei, A.R.: Extended Finite Element Method: Theory and Applications. Wiley Series in Computational Mechanics. Wiley, London (2015)zbMATHGoogle Scholar
  48. 48.
    Wriggers, P.: Computational Contact Mechanics. Springer, Dordrecht (2006)CrossRefzbMATHGoogle Scholar
  49. 49.
    Raijmakers, T.M.J., Vermeltfoort, A.T.: Deformation controlled meso shear tests on masonry piers, Rep. B-92-1156. TU Eindhoven, Build. and Constr. Res., Eindhoven, The Netherlands (1992)Google Scholar
  50. 50.
    Vermeltfoort, A.T., Raijmakers, T.M.J., Janssen, H.J.M.: Shear tests on masonry walls. In: Proceedings of 6th North America Masonry Conference, Philadelphia, USA, pp. 1183–1193 (1993)Google Scholar
  51. 51.
    Lourenço, P.B., Rots, J.G.: Multisurface interface model for analysis of masonry structures. J. Eng. Mech. 123, 660–668 (1997)CrossRefGoogle Scholar
  52. 52.
    Zucchini, A., Lourenço, P.B.: A micro-mechanical homogenisation model for masonry: application to shear walls. Int. J. Solids Struct. 46, 871–886 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Discipline of Civil Engineering, Structural Engineering and Computational Mechanics Group (SECM)University of KwaZulu-NatalDurbanSouth Africa
  2. 2.Faculty of Production Engineering and Management, Institute of Computational Mechanics and OptimizationTechnical University of CreteChaniaGreece

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