Damage Mechanics of Lead-Rubber Bearings Using the Unified Mechanics Theory
Hernandez Morales, Hernan
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In the last few decades, lead-rubber bearings (LRB) have been installed in a number of essential and important structures, like hospitals, universities and bridges, which are located in earthquake-prone areas in the world. The main aim of use of LBR is providing the structure with period lengthening and the capacity of dissipating a considerable amount of earthquake energy to mitigate the damaging effects of strong ground motions. Therefore, studying the damage evolution in this kind of devices is fundamental to understand and accurately describe their mechanical behavior, so that seismically isolated structures can be designed more safely.Up to this point, the literature shows that damage mechanics of LBR has been studied using Newtonian mechanics and empirical degradation equations because Newtonian Mechanics laws only govern what happens to a system at initial load application. Hence, phenomenological curve fitting degradation polynomials must be obtained from experiments. In this thesis, the Unified Mechanics Theory, which integrates Thermodynamics laws and Newtonian Mechanics laws, has been used. As a result, there is no need for that empirical polynomial curve fitting in order to describe the degradation of the initial stiffness. In Unified Mechanics, every nodal point is defined by two variables which cannot exist independently: an unknown displacement and an entropy generation rate. Therefore, the stiffness is continuously degraded or healed according to the entropy production rate at each node.A finite element model of a lead rubber bearing was constructed in ABAQUS, where a user material subroutine UMAT was implemented to define the thermodynamics-based damage mechanics viscoplastic constitutive model of lead. Properties of lead such as the Young’s and shear modulus and the yield strength were obtained from a tensile test of a lead specimen (Kalpakidis and Constantinou, 2008), while others like the stress exponent and the creep activation energy were taken from Gomez, 2006. Moreover, neo-Hookean model was assigned to rubber while steel was considered as having linear elastic behavior.Several force-displacement hysteresis loops were calculated and compared with test data (Constantinou et al, 2007). A very good match with respect to the characteristic strength, energy dissipated per cycle, effective stiffness and effective damping was obtained for the first three loops, particularly for the second. Other important observation was that the damage mechanics model could capture the marked decrease in the energy dissipation capacity when going from the first to the second cycle, which usually occurs in LRB. Finally, the variation of the degradation parameter Φ throughout the simulation was plotted. A simple formula that relates Φ with the number of cycles at the maximum displacement was proposed.