A Nonlinear Beam Macroelement for the In-plane and Out-of-plane Behaviour of Masonry Walls
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The main focus of this study is the simulation of the in- and out-of-plane response of masonry walls in the framework of the macroelement approach. This latter is widely adopted for the analysis of the cyclic response of masonry, combining advanced formulations and constitutive laws, with a related good accuracy of the simulation, with a low computational burden, advantageous especially for dynamic analyses. Indeed, these latter are fundamental for studying existing masonry structures located in seismic prone areas. However, the common approximation given by the assumption of excluding the out-of-plane collapse mechanisms, leads to a lack of reliability in the simulation of the real behaviour, neglecting some relevant mechanisms which may be activated during cyclic loads [1]. The macroelement here presented is an improvement of that proposed in [2] for the two-dimensional simulation of masonry structural behaviour, with the extension to the three-dimensional and the dynamic case. In addition to the nonlinear hinges reproducing the in-plane mechanisms, nonlinear hinges for the out-of-plane states are included in series with a Timoshenko beam element. The hinges, which simulate one-way and two-way bending mechanisms and damage evolution in the out-of-plane direction, are characterized by a nonlinear constitutive law relying on a Bouc-Wen model, enriched with the description of damage and flexibility increase [3]. The in-plane direction sees two flexural hinges and a shear hinge, in series with a Euler-Bernoulli beam element. Pinching effect is also described by means of a nonlinear elastic device in parallel to the Bouc-Wen model. The performance of the described model is validated by means of simulations of cyclic experimental tests on masonry panels available in the literature.