Thesis title: Macromechanical hysteretic models with damage for the analysis of the nonlinear response of historical masonry structures
The study of the behavior of existing masonry structures has certainly been a topic of great interest for long time, especially considering the large number of existing buildings still in use in Italy and in several other Countries, both of historic interest or commonly used, and their high vulnerability particularly when seismic actions are taken into account.
Several modeling approaches have been developed over time, varying the level of detail required in describing the structural response and the amount of input parameters needed. Obviously, the greater the degree of accuracy requested in the behavior description, the more detailed the available information regarding the material and the entire structure shall be. In addition to classical micromechanical, macromechanical, and multi-scale finite element models, however, macro-models are widely adopted approaches, especially between practitioners', and, more specifically, the equivalent frame model. Thanks to the combination of a low computational burden and a reduced number of input parameters, in fact, it is still possible to achieve a good level of accuracy and the possibility to study the response to dynamic actions.
However, the adoption of advanced constitutive laws, appropriate for the material that shall be described, is a crucial prerequisite for the equivalent frame approach to be competitive in masonry modeling with respect to more detailed modeling techniques. Indeed, the description of the characteristic phenomena of the highly nonlinear masonry material, such as the presence of strength and stiffness degradation, as well as plasticity and energy dissipation, cannot be ignored.
At the same time, classical equivalent frame approaches are based on assumptions, at the structural level, that can result overly idealized with respect to the real conditions observable in existing buildings, such as box-like behavior or good connections between walls or between walls and floors. Out-of-plane flexural mechanisms, which can occur very easily, as observed in real structures' behavior under recent earthquake events, are therefore commonly neglected in favor of studying in-plane mechanisms only.
This work focuses its attention, then, on the development of a macroelement applicable in the framework of the equivalent frame approach. First, an enhancement of the modified Bouc-Wen constitutive law presented in Liberatore et al. (2019) is given, proposing the introduction of an additional flexibility increase term to the damage term, with the aim of better reproducing the degrading behavior of masonry panels from a phenomenological point of view. This advanced constitutive law is then implemented in a force-based beam macroelement with lumped nonlinear shear and flexural hinges. A discussion on the degrading behavior in the dynamic field is carried on, as well as different strategies regarding the mass matrix evaluation. Last, the out-of-plane behavior is introduced, focusing on the degradation effects due to one-way and two-way bending mechanisms.
Each implementation is validated through comparison with experimental results available in the literature and, in some cases, with the results obtained through different numerical approaches.
In the end, the results of an experimental campaign involving a masonry wall and an unreinforced masonry prototype building are also reproduced. The capability of the model to describe the characteristics of real existing masonry structures is then tested and confirmed.