E. BERTOLESI (1), G. MILANI (2)
(1) PhD, Department of Architecture, Built Environment and Construction Engineering (ABC), Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
(2) Associate professor, Department of Architecture, Built Environment and Construction Engineering (ABC), Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
In the present paper, a simple homogenisation two-step procedure is proposed for the analyses of both in and out of plane loaded masonry walls and 3D structures. The “unit cell” is discretized with 24 triangular plane constant stress (CST) elements and interfaces. Bricks are specified to behave elastically, whereas mortar joints are set as zero thickness non-linear interfaces. The mechanical response of joints is modelled with different holonomic relationships including two dominant failure modes, namely cracking (mode I) and shear (mode II), or a combination of both (mixed mode). In particular, either a piecewise linear or an improved version of the Xu-Needleman exponential law are used, both exhibiting post peak softening. At the structural level, the homogenisation model is implemented into general purpose commercial FE software, modelling the homogenized orthotropic continuum as a discrete assemblage of Rigid Bodies and Homogenized softening Springs (HRBSM). In such a rigid element model, a variety of springs are introduced, to properly characterize both the in plane homogenized shear and normal behaviour, as well as bending and torque (out of plane behaviour). Moment-curvature relationships are evaluated simply by on thickness integration from the knowledge of in plane homogenized stress-strain relationships. Mechanical properties of homogenized springs are identified via classic energetic identification. Three case studies of technical relevance are finally presented for benchmarking purposes: (i) a windowed shear panel, (ii) a church façade modelled with a portion of the perpendicular walls and (ii) a 3D half scale two story masonry building.