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Abstract: Starting from the micro-structural definition of the stress tensor, Rothenburg and Bathurst (1989) derived a stress–force–fabric relationship for granular materials by approximating the directional distributions of the fabric, more specifically, the contact normal density distribution in this paper and the contact forces with Fourier functions and integrating over directions. This paper aims to assess the validity of the two key assumptions made during their derivation using particle-based numerical simulation in the cases of proportional loading and non-proportional loading. These two assumptions are (i) the 2nd-rank Fourier functions adopted are good enough to approximate the directional distributions of contact normal densities and contact forces and (ii) the principal directions of contact forces and contact normal density are coaxial. Numerical simulations have been carried out to conduct virtual experiments on the behaviour of isotropic specimens to monotonic loading, of isotropic specimens to stress rotation, and of anisotropic specimens to monotonic loading. The first one stands for the case of proportional loading while the latter two are non-proportional loading paths involving rotation of the frame of principal stresses and the frame of fabric, respectively. The directional distributions of contact normal density and contact forces are traced during these three typical loading processes. The simulation results indicate that the 2nd-rank Fourier functions give reasonable approximations, while the coaxial assumption is generally not valid in non-proportional loading. In the case that the principal directions of contact normal density and contact force differ, a more general expression of the stress–force–fabric relationship is required. This research can help to improve our understanding of the stress state and hence shear strength of granular materials based on the particle scale investigation. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]