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**An enhanced multi-scale approach for masonry wall computations with localization of damage.**
*(English)*
Zbl 1194.74283

Summary: This contribution presents a multi-scale framework for the computational study of masonry structures. In order to overcome the need for excessively complex closed-form constitutive equations, a first-order computational homogenization framework is applied to infer the nonlinear material behaviour of brick masonry in the presence of quasi-brittle damage. A localization analysis is carried out based on the macroscopic homogenized tangent stiffness. It is shown that localization is detected along preferential orientations, which are consistent with the underlying mesostructural failure patterns and with the applied loading. The macroscopic description is enhanced with a finite width damage band model in order to allow the treatment of macroscopic localization resulting from damage growth in the constituents. As a result of the use of homogenization techniques on finite volumes and the presence of quasi-brittle constituents, mesostructural snap-back may occur in the homogenized material response. A methodology to introduce this type of response in the multi-scale technique is proposed. The numerical implementation of the multi-scale solution scheme using a finite element method is outlined. The results obtained by the framework are illustrated by means of elementary examples, and by an example of a structural wall computation.

### Keywords:

multi-scale modelling; masonry; computational homogenization; damage-induced anisotropy; localization; embedded discontinuities; snap-back; structural computations
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\textit{T. J. Massart} et al., Int. J. Numer. Methods Eng. 69, No. 5, 1022--1059 (2007; Zbl 1194.74283)

### References:

[1] | Experimental and numerical issues in the modelling of the mechanical behaviour of masonry. In Structural Analysis of Historical Constructions II, , , (eds). CIMNE: Barcelona, 1998; 57–91. |

[2] | Lourenço, Progress in Structural Engineering and Materials 4 pp 301– (2002) |

[3] | Massart, European Journal of Mechanics – A/Solids 23 pp 719– (2004) |

[4] | Lourenço, Journal of Engineering Mechanics 123 pp 660– (1997) |

[5] | Giambanco, Computer Methods in Applied Mechanics and Engineering 190 pp 6493– (2001) |

[6] | Lourenço, International Journal for Numerical Methods in Engineering 40 pp 4033– (1997) |

[7] | Berto, International Journal for Numerical Methods in Engineering 55 pp 127– (2002) |

[8] | Papa, Applied Mathematics Modelling 21 pp 319– (1997) |

[9] | Halm, Archive of Applied Mechanics 72 pp 498– (2002) |

[10] | Anthoine, International Journal of Solids and Structures 32 pp 137– (1995) · Zbl 0868.73010 |

[11] | Cecchi, European Journal of Mechanics – A/Solids 21 pp 249– (2001) |

[12] | Anthoine, Communications in Numerical Methods in Engineering 13 pp 319– (1997) |

[13] | Pegon, Computers and Structures 64 pp 623– (1997) |

[14] | Toughness of heterogeneous polymeric systems. A modelling approach. Ph.D. Thesis, Eindhoven University of Technology, 1998. |

[15] | Feyel, Computer Methods in Applied Mechanics and Engineering 183 pp 309– (2000) |

[16] | Kouznetsova, International Journal for Numerical Methods in Engineering 54 pp 1235– (2002) |

[17] | Luciano, International Journal of Solids and Structures 34 pp 3191– (1997) |

[18] | van der Pluijm R. Out-of-plane bending of masonry–behaviour and strength. Ph.D. Thesis, Eindhoven University of Technology, 1999. |

[19] | de Borst, Engineering Computations 10 pp 99– (1993) |

[20] | Kouznetsova, Computational Mechanics 27 pp 37– (2001) |

[21] | Smit, Computer Methods in Applied Mechanics and Engineering 155 pp 181– (1998) |

[22] | van der Sluis O. Homogenisation of structured elastoviscoplastic solids. Ph.D. Thesis, Eindhoven University of Technology, 2001. |

[23] | Massart, Engineering Fracture Mechanics 72 pp 1238– (2005) |

[24] | Peerlings, International Journal for Numerical Methods in Engineering 39 pp 3391– (1996) |

[25] | Rupture et calculs à la ruine. These d’habilitation, Université Paris VI Pierre et Marie Curie–LMT ENS Cachan, 1991 (in French). |

[26] | Toupin, Archives of Rational Mechanics and Analysis 11 pp 385– (1962) |

[27] | Mindlin, Archives of Rational Mechanics and Analysis 16 pp 51– (1964) · Zbl 0119.40302 |

[28] | The localisation of plastic deformations. In Theoretical and Applied Mechanics, (ed.). North-Holland Publishing Company: Amsterdam, 1976. |

[29] | Rice, International Journal of Solids and Structures 16 pp 597– (1980) |

[30] | Geers, International Journal for Numerical Methods in Engineering 46 pp 177– (1999) |

[31] | Multi-scale modeling of damage in masonry structures. Ph.D. Thesis, Eindhoven University of Technology & Université Libre de Bruxelles, 2003. |

[32] | Sluys, International Journal of Solids and Structures 35 pp 4257– (1998) |

[33] | Jirásek, Computer Methods in Applied Mechanics and Engineering 188 pp 307– (2000) |

[34] | de Borst, Engineering Computations 18 pp 241– (2001) |

[35] | Discontinuous modelling of strain localisation and failure. Ph.D. Thesis, Delft University of Technology, 2001. |

[36] | Evers, Journal of Mechanics and Physics of Solids 50 pp 2403– (2002) |

[37] | Massart, Comptes-Rendus Mécanique 333 pp 1– (2005) |

[38] | Path-following constraint based on fracture energy control. In Proceedings of the VII International Conference on Computational Plasticity–COMPLAS 2003, (eds). CIMNE: Barcelona, 2003. |

[39] | Computational homogenisation for the multi-scale analysis of multi-phase materials. Ph.D. Thesis, Eindhoven University of Technology, 2002. |

[40] | . Deformation controlled tests in masonry shear walls. Technical Report B-92-1156, TNO–Bouw, Delft, The Netherlands, 1992 (in Dutch). |

[41] | Computational strategies for masonry structures. Ph.D. Thesis, Delft University of Technology, 1996. |

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.