Issue 29

G. Gianbanco et alii, Frattura ed Integrità Strutturale, 29 (2014) 150-165; DOI: 10.3221/IGF-ESIS.29.14 150 Focussed on: Computational Mechanics and Mechanics of Materials in Italy CH of masonry materials via meshless meso-modeling Giuseppe Giambanco, Emma La Malfa Ribolla, Antonino Spada Department of Civil, Environmental, Aerospace and Materials Engineering (DICAM) - University of Palermo giuseppe.giambanco@unipa.it , emmalamalfa@hotmail.it, antonino.spada@unipa.it A BSTRACT . In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Method (MM) is adopted to solve the BVP at the mesoscopic level. The work focuses on the BVP solution. The consistent tangent stiffness matrix at a macroscopic quadrature point is evaluated on the base of BVP results for the UC together with a localisation procedure. Validation of the MM procedure at the meso-scale level is demonstrated by numerical examples that show the results of the BVP for the simple cases of normal and shear loading of the UC. K EYWORDS . Multiscale; Mesomodeling; Meshless; Masonry. I NTRODUCTION odeling of structures constituted by heterogeneous materials, as masonry and composite laminates, is still one of the most complex and challenging matters of the modern structural engineering. Anisotropy, asymmetry, geometrical and material non-linearities are the main features of the mechanical behavior to be considered in the formulation of the structural model. In masonry structures the most relevant kinematical and mechanical phenomena take place at a scale which is small if compared to the dimensions of the structure. On the other side, the structure is governed, in its peculiar overall response, by its global geometrical and morphological configuration. In literature, two different scales of interest are distinguished, directly linked to as many theoretical approaches: the mesoscopic approach a nd the macroscopic approach . The mesoscopic approach considers units and their interfaces individually. Most of the efforts in this research area are concentrated on the formulation of advanced interface constitutive laws capable to describe the damage evolution and the onset of irreversible strains and related coupled effects for different mechanical problems. In Giambanco et al. [1] the masonry material is considered as an assembly of units in contact by means of elastoplastic zero-thickness interfaces, focusing on the cohesive-frictional joint transition. Lourenço and Rotz [2] proposed a joint failure criterion which adopts a cap model to take into account the mortar compaction due to high compressive stresses. Alfano and Sacco [3] introduced a damage-plasticity interface model that discriminated a linear elastic undamaged zone from a damaged zone with an unilateral Coulomb friction law. More recently, Spada et al. [4] and Sacco and Lebon [5] concentrated in the formulation of interface laws which include the non-linear effects of stiffness M