A three-dimensional cyclic meso-scale numerical procedure for simulation of unreinforced masonry structures

Three-dimensional (3D) cyclic analysis and constitutive material model are needed to better understand the behavior of unreinforced masonry (URM) buildings under earthquake excitations. So far, most of the existing constitutive material models applied to the field of masonry structures have focused on two-dimensional modeling and monotonic loading. In addition, most of the studies have used implicit dynamic procedures in the time domain. Based on the inherent features of implicit formulations for nonlinear problems, a number of iterations are required at each time step to achieve convergence, which leads to intensive computations and lack of convergence in some cases such as cyclic loadings. In this paper, a 3D cyclic constitutive material model implemented within an explicit analysis procedure is proposed, which can be used to model large deformation behavior of masonry walls. A rigorous constitutive material model is proposed and validated with available experimental data from previous researches, and for the attributes for which experimental data is not readily available; a number of new experimental tests has been conducted by the authors. The material model is implemented in a user-defined subroutine and compiled with ABAQUS (VUMAT). The subroutine is then tested by several numerical examples on a single element under cyclic normal and transverse deformations to examine the behavior of the material model. Moreover, several analyses are conducted and the numerical results are compared with experimental data to assess the robustness and predictive capabilities of the proposed material model and the numerical solution algorithms.