Secondly, to generate a hysteresis behavior, a damping coefficient is applied to the spring so that the model can fit the experimental data. In the experiment \cite{toopchi2008testing}, the equivalent damping of the unbonded FREI-200 was reported to be equal to 5.2%. The spring model with damping (fig. \ref{249858}b) shows a reasonable fitting with the experiment (fig. \ref{887768}a). However, it cannot catch up the sudden increase of damping as seen in the last cycle of the experiment. Nevertheless, it is noted that this limitation does not affect the final results. With the same procedure, a spring model of UFREI-175 is obtained (fig. \ref{249858}c). The nonlinear spring model of UFREI-175 is implemented later at the structural level of a two-story isolated masonry building.
Seismic performance of an isolated masonry housing using UFREIs
An FE model of a medium size two-story masonry house with openings and concrete diaphragms at foundation and roof levels is implemented in ABAQUS commercial code. The masonry building taken as reference is an existing one and was constructed in Tawang, India \cite{thuyet2017mitigation} to test the behavior of masonry houses isolated with UFREIs. According to authors’ knowledge, this is probably one of the first examples of masonry housing isolation by means of low cost devices. Dimensions of the building are the following: thickness of the walls 300 mm, each room has 4 x 4 m plan dimensions, height of each floor is 3m, see Fig. \ref{690461}. To prevent premature damage of the walls, rigid beams on top of windows and doors are inserted, in agreement with the real prototype. The numerical model has thinner walls and significantly smaller isolators compared to the real one built in India \cite{thuyet2017mitigation}.