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The creation of an effective, accurate finite element mesh is crucial for running whatsoever numerical analysis on structural models. This is especially true when micro-scale, mesoscale, and homogenization-based approaches are used, since they involve a precise and distinct representation of the constitutive materials. One fitting example is embodied by masonry with irregular bond, where blocks are randomly assembled and often present different shapes and dimensions. This work presents a Matlab script for the generation of a full 3D finite element mesh, which is created directly from a simple rasterized picture of the masonry element under investigation. A voxel approach is here used, where one pixel of the image is turned into one solid finite element. The resulting 3D mesh is employed into a broader Matlab script which derives homogenized failure surfaces for masonry test-windows. In particular, the effectiveness of the 3D mesh is validated by comparing the homogenized failure surfaces obtained for an in-plane loaded masonry panel to those retrieved from the 2D version of the script with a 2D mesh, whose reliability has already been established.The creation of an effective, accurate finite element mesh is crucial for running whatsoever numerical analysis on structural models. This is especially true when micro-scale, mesoscale, and homogenization-based approaches are used, since they involve a precise and distinct representation of the constitutive materials. One fitting example is embodied by masonry with irregular bond, where blocks are randomly assembled and often present different shapes and dimensions. This work presents a Matlab script for the generation of a full 3D finite element mesh, which is created directly from a simple rasterized picture of the masonry element under investigation. A voxel approach is here used, where one pixel of the image is turned into one solid finite element. The resulting 3D mesh is employed into a broader Matlab script which derives homogenized failure surfaces for masonry test-windows. In particular, the effectiveness of the 3D mesh is validated by comparing the homogenized failure surfaces obtained for an i...

Due to the need for seismic protection in developing countries, some investigations on low-cost seismic isolators have been performed. One of them is an unbonded fiber reinforced elastomeric isolator (UFREI), in which the bearing is not bonded to the supports. This type allows the application of base isolation without any expensive thick-steel plate for supports. The UFREI is considerably effective for utilization on low-rise buildings, even masonry housings. Advantageous features of the UFREI are the roll-over and full-contact deformations. The former can decrease the effective stiffness of the isolation system, lowering the seismic force demand. Meanwhile, the latter plays a role in generating a hardening effect, limiting the shear displacement of the base isolation under a maximum earthquake. Those remarkable advantages reveal a great potency of world-wide application of UFREIs. However, there is no representative model of UFREI in the various software of structural analyses. In this work, a comprehensive but simple model of UFREI is implemented in an ABAQUS user element (UEL), taking into account the softening, hardening, and hysteresis effects of the bearing. In addition, multiple DOFs are considered to characterize the complex 3D behavior of a UFREI in lateral, axial, rotations, and torsion. The results show that the UEL model can reasonably fit the finite element model of a referenced UFREI. The proposed UEL model is helpful in 3D analyses of isolated structures using UFREIs.

The paper provides an insight into the seismic strengthening of masonry towers with horizontal and vertical steel rods by means of a limit analysis approach. The kinematic theorem of limit analysis with five pre-assigned failure mechanisms, observed during post-earthquake surveys, has been implemented for different geometries of idealized towers, aimed to cover a wide range of real masonry towers. Different mechanisms can activate as a consequence of the geometric features in combination with masonry mechanical properties. The possible introduction of horizontal and vertical steel rods is investigated in the same way, simply considering in limit analysis computations the contribution of the reinforcement in the internal dissipation. Thanks to the simplicity of the limit analysis approach, large scale Monte Carlo (MC) simulations with several geometries are carried out. Results show that, depending on the geometry of the tower and the mechanical properties of masonry, different mechanisms can be active and...

The paper presents some seismic analyses on three masonry churches located in Emilia-Romagna (Italy), recently stricken by a devastating earthquake sequence from 20th to 29th May 2012. These churches have a similar geometrical configuration, consisting of three naves, a central colonnade and a simple apse. Limit analyses are conducted on the most important macro-elements of the structure and a full investigation of the churches is carried out by means of the commercial FE Code SAP2000, in both linear and non-linear ranges. Two accelerograms are considered: one is defined in accordance with Italian code response spectrum and the other is based on a natural record of the 29th May earthquake. For both scenarios, the seismic behaviour of the churches is analysed in detail and some vulnerability considerations are drawn. A remarkable consistency is found between limit analyses of macro-elements and response spectrum analyses, whilst some discrepancies can be noted for non-linear dynamic analyses. The results p...

Masonry structures with fictile tubules were a distinctive building technique of the Mediterranean area. This technique dates back to Roman and early Christian times, used to build vaulted constructions and domes with various geometrical forms by virtue of their modular structure. In the present work, experimental tests were carried out to identify the mechanical properties of hollow clay fictile tubules and a possible reinforcing technique for existing buildings employing such elements. The experimental results were then validated by devising and analyzing numerical models with the FE software Abaqus, also aimed at investigating the structural behavior of an arch via linear and nonlinear static analyses.

Rubber isolators are used widely in constructions which require a vibration or seismic isolation. It consists of rubber layers and reinforcements that can be steel or fiber lamina. The fiber reinforced isolator results in a lower cost of production and application than that of steel. Using fiber reinforced isolator allows us to make an unbonded model of rubber bearing. This model leads to a smaller horizontal stiffness and larger displacement of isolators. Researchers consider the Unbonded Fiber Reinforced Elastomeric Isolator (U-FREI) as a low-cost form of rubber bearings. U-FREIs are suitable to isolate seismically a masonry building, which is a common type of housing in developing countries. In this work, we present a finite element model (FEM) to predict the behavior of the U-FREIs undergoing moderate deformations. We adopt a Yeoh hyperelasticity model which is available in the standard package of Abaqus FE software and estimate its coefficients through the available experimental data. Then, we apply that isolation system onto masonry housing with some simplified methods. We also observe the horizontal behaviors of U-FREIs under different vertical loads and consider a critical condition when the isolators start to be unstable. In parallel, we perform an analytical model to predict the shear behavior and the deformation limit of isolators. Finally, the results show that the analytical model is sufficiently accurate compared to the FE analyses.Rubber isolators are used widely in constructions which require a vibration or seismic isolation. It consists of rubber layers and reinforcements that can be steel or fiber lamina. The fiber reinforced isolator results in a lower cost of production and application than that of steel. Using fiber reinforced isolator allows us to make an unbonded model of rubber bearing. This model leads to a smaller horizontal stiffness and larger displacement of isolators. Researchers consider the Unbonded Fiber Reinforced Elastomeric Isolator (U-FREI) as a low-cost form of rubber bearings. U-FREIs are suitable to isolate seismically a masonry building, which is a common type of housing in developing countries. In this work, we present a finite element model (FEM) to predict the behavior of the U-FREIs undergoing moderate deformations. We adopt a Yeoh hyperelasticity model which is available in the standard package of Abaqus FE software and estimate its coefficients through the available experimental data. Then, we apply ...

The present paper is devoted to the discussion of a series of unreinforced and FRP retrofitted panels analyzed adopting the Rigid Body and Spring-Mass (HRBSM) model developed by the authors. To this scope, a total of four out of plane loaded masonry walls tested up to failure are considered. At a structural level, the non-linear analyses are conducted replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage by means of which out of plane mechanisms are allowed. FRP retrofitting is modeled adopting two noded truss elements whose mechanical properties are selected in order to describe possible debonding phenomenon or tensile rupture of the strengthening. The outcome provided numerically are compared to the experimental results showing a satisfactory agreement in terms of global pressure-deflection curves and failure mechanisms.

Two finite element homogenized-based strategies are presented for the out-of-plane behaviour characterization of an English bond masonry wall. A finite element micro-modelling approach using Cauchy stresses and first order movements are assumed for both strategies. The material nonlinearity is lumped on joints interfaces and bricks are considered elastic. Nevertheless, the first model is based on a Plane-stress assumption, in which the out-of-plane quantities are derived through on-thickness wall integration considering a Kirchhoff-plate theory. The second model is a tridimensional one, in which the homogenized out-of-plane quantities can be directly derived after solving the boundary value problem. The comparison is conducted by assessing the obtained out-of-plane bending-and torsion-curvature diagrams. A good agreement is found for the present study case., This work was supported by FCT (Portuguese Foundation for Science and Technology), within ISISE, scholarship SFRH/BD/95086/2013. This work was also partly financed by FEDER funds through the Competitivity Factors Operational Programme - COMPETE and by national funds through FCT - Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-007633., info:eu-repo/semantics/publishedVersion

A Finite element model was established to examine performance of a low-cost friction base-isolation system in reducing seismic vulnerability of rural buildings. This study adopts an experimental investigation of the isolation system which was conducted in India. Four friction isolation interfaces, namely, marble-marble, marble-high-density polyethylene, marble-rubber sheet, and marble-geosynthetic were involved. Those interfaces differ in static and dynamic friction coefficient obtained through previous research. The FE model was performed based on a macroscopic approach and the masonry wall is assumed as an isotropic element. In order to observe structural response of the masonry house, elastic and plastic parameters of the brick wall were studied. Concrete damage plasticity (CDP) model was adopted to determine non-linear behavior of the brick wall. The results of FE model shows that involving these friction isolation systems could much decrease response acceleration at roof level. It was found that systems with marble-marble and marble-geosynthetic interfaces reduce the roof acceleration up to 50% comparing to the system without isolation. Another interesting result is there was no damage appearing in systems with friction isolation during the test. Meanwhile a severe failure was clearly visible for a system without isolation.A Finite element model was established to examine performance of a low-cost friction base-isolation system in reducing seismic vulnerability of rural buildings. This study adopts an experimental investigation of the isolation system which was conducted in India. Four friction isolation interfaces, namely, marble-marble, marble-high-density polyethylene, marble-rubber sheet, and marble-geosynthetic were involved. Those interfaces differ in static and dynamic friction coefficient obtained through previous research. The FE model was performed based on a macroscopic approach and the masonry wall is assumed as an isotropic element. In order to observe structural response of the masonry house, elastic and plastic parameters of the brick wall were studied. Concrete damage plasticity (CDP) model was adopted to determine non-linear behavior of the brick wall. The results of FE model shows that involving these friction isolation systems could much decrease response acceleration at roof level. It was found that syst...

This paper investigates the effectiveness of reducing the seismic vulnerability of masonry towers by means of innovative and traditional strengthening techniques. The followed strategy for providing the optimal retrofitting for masonry towers subjected to seismic risk relies on preventing active failure mechanisms. These vulnerable mechanisms are pre-assigned failure patterns based on the crack patterns experienced during the past seismic events. An upper bound limit analysis strategy is found suitable to be applied for simplified tower models in their present state and the proposed retrofitted ones. Taking into consideration the variability of geometrical features and the uncertainty of the strengthening techniques, Monte Carlo simulations are implemented into the limit analysis. In this framework a wide range of idealized cases are covered by the conducted analyses. The retrofitting strategies aim to increase the shear strength and the overturning load carrying capacity in order to reduce vulnerability. This methodology gives the possibility to use different materials which can fulfill the structural implementability requirements.

Many existing reinforced concrete buildings in Southern Europe were built (and hence designed) before the introduction of displacement based design in national seismic codes. They are obviously highly vulnerable to seismic actions. In such a situation, simplified methodologies for the seismic assessment and retrofitting of existing structures are required. In this study, a displacement based procedure using non-linear static analyses is applied to a four-story existing RC frame. The aim is to obtain an estimation of its overall structural inadequacy as well as the effectiveness of a specific retrofitting intervention by means of GFRP laminates and RC jacketing. Accurate numerical models are developed within a displacement based approach to reproduce the seismic response of the RC frame in the original configuration and after strengthening.

A simple quasi analytical holonomic homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how homogenized stress-strain behavior can be evaluated semi-analytically.

The simple quasi analytical holonomic homogenization approach for the non-linear analysis of in-plane loaded masonry presented in Part 1 is here implemented at a structural leveland validated. For such implementation, a Rigid Body and Spring Mass model (RBSM) is adopted, relying into a numerical modelling constituted by rigid elements interconnected by homogenized inelastic normal and shear springs placed at the interfaces between adjoining elements. Such approach is also known as HRBSM. The inherit advantage is that it is not necessary to solve a homogenization problem at each load step in each Gauss point, and a direct implementation into a commercial software by means of an external user supplied subroutine is straightforward. In order to have an insight into the capabilities of the present approach to reasonably reproduce masonry behavior at a structural level, non-linear static analyses are conducted on a shear wall, for which experimental and numerical data are available in the technical literature....

The paper aims at studying the possible interaction between two different accelerators (DPG and TBBS) in the chemical kinetic of Natural Rubber (NR) vulcanized with sulphur. Two different numerical meta-models, which belong to the family of the so-called response surfaces RS are compared. The first is linear against TBBS and DPG and therefore well reproduces no interaction between the accelerators, whereas the latter is quadratic with bilinear term. The numerical meta- models are calibrated on the experimental data obtained by using the same mixture with several DPG and TBBS concentrations, varying the curing temperature in the range 150-180 ◦ C and obtaining rheometer curves with a step of 10 ◦ C. In order to study any possible interaction between the two accelerators - and eventually evaluating its engineering relevance - rheometer data are normalized by means of the well-known Sun and Isayev normalization approach and two output parameters are assumed as meaningful to have an insight into the possible interaction, namely time at maximum torque and reversion percentage. Both RSs are deduced from standard best fitting of experimental data available. It is found that, generally, there is a sort of interaction between TBBS and DPG, but that the error introduced making use of a linear model (no interaction) is generally lower than 10%, i.e. fully acceptable from an engineering standpoint.

A simple homogenized rigid body and spring model (HRBSM) is presented and applied for the non-linear dynamic analysis of 3D masonry structures. The approach, previously developed by the authors for the modeling of in-plane loaded walls is herein extended to real 3D buildings subjected to in- and out-of-plane deformation modes. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. All the simulations here presented are performed using the commercial software Abaqus. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church facade and an in-scale masonry building, both subjected to dynamic excitation. The...

A heterogeneous full 3D non-linear FE approach is validated against experimental results obtained on an in-scale masonry cross vault assembled with dry joints, and subjected to various loading conditions consisting on imposed displacement combinations to the abutments. The FE model relies into a discretization of the blocks by means of few rigid-infinitely resistant parallelepiped elements interacting by means of planar four-noded interfaces, where all the deformation (elastic and inelastic) occurs. The investigated response mechanisms of vault are the shear in-plane distortion and the longitudinal opening and closing mechanism at the abutments. After the validation of the approach on the experimentally tested cross-vault, a sensitivity analysis is conducted on the same geometry, but in real scale, varying mortar joints mechanical properties, in order to furnish useful hints for safety assessment, especially in presence of seismic action.

This study presents some results of a comprehensive numerical analysis on three masonry churches damaged by the recent Emilia-Romagna (Italy) seismic events occurred in May 2012. The numerical study comprises: (a) pushover analyses conducted with a commercial code, standard nonlinear material models and two different horizontal load distributions; (b) FE kinematic limit analyses performed using a non-commercial software based on a preliminary homogenization of the masonry materials and a subsequent limit analysis with triangular elements and interfaces; (c) kinematic limit analyses conducted in agreement with the Italian code and based on the a-priori assumption of preassigned failure mechanisms, where the masonry material is considered unable to withstand tensile stresses. All models are capable of giving information on the active failure mechanism and the base shear at failure, which, if properly made non-dimensional with the weight of the structure, gives also an indication of the horizontal peak ground acceleration causing the collapse of the church. The results obtained from all three models indicate that the collapse is usually due to the activation of partial mechanisms (apse, facade, lateral walls, etc.). Moreover the horizontal peak ground acceleration associated to the collapse is largely lower than that required in that seismic zone by the Italian code for ordinary buildings. These outcomes highlight that structural upgrading interventions would be extremely beneficial for the considerable reduction of the seismic vulnerability of such kind of historical structures.

The paper addresses the topic of the numerical analysis up to collapse of masonry vaults. At this aim, an advanced numerical model is utilized, which requires the discretization of the structure by means of three dimensional six-noded wedge finite elements rigid and infinitely resistant and interfaces exhibiting a non linear behavior with softening. The incremental problem is solved by means of a robust quadratic programming procedure and interfaces mechanical properties are estimated by means of a consolidated homogenization strategy. Failure mechanisms and collapse loads are evaluated numerically for a case study in Italy (a masonry cross vault subjected to increasing vertical live loads up to collapse), varying mechanical properties of the vault and considering the stabilizing role played by the backfill. In light of the results obtained, limitations and possibilities of the widely diffusedtraditional approaches based on the subdivision of the vault into a series of arches are addressed.

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a combined experimental and numerical homogenizedapproach. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine. In parallel, a wide experimental campaign is conducted on walls in two way bending, with the double aim of both validating the numerical model and investigating the behavior of walls that may not be reduced to simple cantilevers or simply supported beams. Panels investigated are dry-joint in scale square walls simply supported at the base and on a vertical edge, exhibiting the classical Rondelet’s mechanism. The results obtained are compared with those provided by the numerical model.

The main problem in the industrial production process of thick EPM/EPDM elements is constituted by the different temperatures which undergo internal (cooler) and external regions. Indeed, while internal layers remain essentially under-vulcanized, external coating is always over-vulcanized, resulting in an overall average tensile strength insufficient to permit the utilization of the items in several applications where it is required a certain level of performance. Possible ways to improve rubber output mechanical properties include a careful calibration of exposition time and curing temperature in traditional heating or a vulcanization through innovative techniques, such as microwaves. In the present paper, a comprehensive numerical model able to give predictions on the optimized final mechanical properties of vulcanized 2D and 3D thick rubber items is presented and applied to a meaningful example of engineering interest. A detailed comparative numerical study is finally presented in order to establish pros and cons of traditional vulcanization vs microwaves curing.