Mechanical behaviour of particle composite materials is growing of interest to engineering applications. A computational homogenization procedure in conjunction with a statistical approach have been successfully adopted for the definition of the representative volume element (RVE) size, that in random media is an unknown of the problem, and of the related equivalent elastic moduli. Drawback of such a statistical approach to homogenization is the high computational cost, which prevents the possibility to perform series of parametric analyses. In this work, we propose a so-called fast statistical homogenization procedure (FSHP) developed within an integrated framework that automates all the steps to perform. Furthermore within the FSHP, we adopt the numerical framework of the virtual element method for numerical simulations to reduce the computational burden. The computational strategies and the discretization adopted allow us to efficiently solve the series (hundreds) of simulations and to rapidly converge to the RVE size detection.

In the last decades the modeling of masonry structures has become an argument particularly appealing for many researchers and a large variety of numerical techniques have been formulated with the aim to produce practical applications in civil engineering, with special reference to the preservation and restoration of cultural heritage. Nevertheless, the question appears today still far from being resolved in a general way. The characteristics of frailty, heterogeneity and anisotropy of masonry, as well as the extreme variety of the building/construction rules strongly compromise the possibility of a unified description of its mechanical behavior. In this work a comparison of different models and techniques for the assessment of the mechanical behavior of two-dimensional block masonry walls subjected to the static action of in-plane loads is presented. Different approaches and numerical models are considered: a Limit Analysis approach (LA), a FEM/DEM procedure and a non-linear heterogeneous Finite Element analysis (FE). In particular, the Limit Analysis is able to provide fast and reliable results in term of collapse multiplier and related mechanism. Here a standard Limit Analysis is adopted via a homemade procedure based on Linear Mathematical Programming, considering friction at interfaces. Analyses are performed referring to benchmark examples from literature.

Among the most characteristic structures in historical constructions for crossing large spans are the masonry vaulted structures by utilizing their geometric stability to safely transfer the loads to supports with regard to their negligible tensile strength. The ability of masonry piers to bear such transferred stresses and safely convey them to the support is directly related to their structural integrity, as well as to a number of other factors. Using an in-house limit analysis code, a study on the crucial parameters impacting the safety level of piers under the thrust of arches is performed. Parameters such as pier texture, joint friction angle, and arch shallowness, namely, shallow, semi-circular, and pointed arches, were investigated under three load scenarios: horizontal and concentrated vertical live load applied at mid-span and quarter-span. The main findings of this work show that all studied parameters have a significant influence on the structure response. Higher friction values, sharper arches, and piers that follow the rule of art result in higher collapse multipliers. Furthermore, this work emphasizes the importance of accounting for the sliding mechanism and masonry texture, parameters that are often neglected.

Historical masonry structures have a great interest in civil engineering because they constitute a large part of the world’s building heritage. In this paper, the effects that different geometrical (panel ratio, block ratio, and bond type) and mechanical (friction ratio) parameters have on the in-plane structural response of brick masonry panels are investigated. A discrete modeling approach, based on a limit analysis and capable of reproducing sliding mechanisms, formulation by one of the authors has been adopted, enhanced, and implemented. Results, in terms of collapse multipliers and collapse mechanisms, are presented and analyzed following a systematic statistical approach. Statistically significant effects have been found for each factor considered. Furthermore, the statistical model adopted included nonlinear terms that allowed the identification of whether the effect of one parameter on the response depends on the level of any other parameters. Thus, it was observed that two-way factor interactions played an important role in the in-plane response of masonry panels. The panel ratio-friction ratio two-way factor interaction was the one with a more significant effect.