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In this study, a nonlinear 2D rigid body spring model (RBSM) was developed to verify the experimental works of Carbon Fiber Reinforced Polymer (CFRP) sheets and rods strengthened reinforced concrete (RC) T-shape beam (RC T-beam) section under a combination of bending and shearing loads. Modified Mohr–Coulomb criteria were adopted for modeling the plastic damage of concrete material. The orthotropic smeared layers representing the steel and CFRP materials were laminated on the concrete surface to model the reinforcing steel bars, stirrup steel, and CFRP sheets and rods. A mechanical behavior-based approach to fit the experimental results was discussed using the numerical results at each calibration stage. This study shows how the gradient of compressive and ultimate tensile strength of concrete affects the initial flexure behavior of the load-displacement curve of an RC T-beam. In contrast with finite element modeling, the RBSM can exhibit the crack propagation processes of element separation during the simulation. The calibrations showed the agreement of the models used in predicting the flexural behavior, ultimate load, and strengthening effects of the CFRP sheets and rods to the RC T-beam under bending loads. A systematic calibration procedure combined with the recommended use of energy-based criteria to evaluate the results of calibrated load-displacement curve was proposed. [ABSTRACT FROM AUTHOR]

Bridge beams with half-joint (dapped) ends are common in the design of reinforced concrete and prestressed concrete bridges because they offer convenience in construction work. However, improper rebar detailing and placement in the area of the half-joint, or nib, during construction can make the structure susceptible to crack propagation and deterioration, as well as a potential change in failure mode. This study aims to examine the local behavior of half-joint structures with different rebar arrangements by implementing a three-dimensional discrete meso-scale analytical model, using the rigid body spring model (RBSM) to simulate an experiment conducted in the past. Discrete mesoscopic analysis is chosen for its ability to simulate damage that takes the form of local discontinuities and because rebar geometry can be modeled accurately. It also offers the potential for directly investigating internal stresses and cracks. Results from the implemented simulation models agree well with the reported experimental results. All reinforcement arrangements behave similarly in the elastic region before the cracking load is reached. Thereafter, following the appearance of flexural cracks in the full-depth section and a crack at the re-entrant corner, behavior in terms of load-displacement relationships, crack propagation and internal stresses differs with reinforcement details. The role of each type of reinforcement during crack propagation and in load-carrying behavior is revealed by the simulations. • The contribution of each reinforcement type during loading is presented. • Different rebar layouts result in different post-crack behavior of dapped ends. • The effect of rebar arrangement occurrences on the internal stress and crack pattern. • Difference of failure process is studied through the RBSM simulations. • Diagonal rebar effectively increases capacity and prevents crack development. [ABSTRACT FROM AUTHOR]

Concrete breakout failures with acutely damaged concrete are one of the main problems caused by expansion anchors under tensile loading. In this study, the prevention of concrete breakout is investigated by post-installed reinforcement (PRs). Experimental and numerical studies were conducted to look into the effect of the PRs on the expansion anchors subjected to tensile loads. The 3D Rigid Body Spring Model (RBSM), which is based on discrete analysis at the mesoscale, was used as supporting numerical research. On pullout capacity, displacement, failure mechanism, and concrete breakout geometry, both experimental and numerical analyses were undertaken. The numerical analysis also looked at internal stress, strain, and concrete cracking. In general, the anchors with the PRs had steady displacement (ductile) and less brittle failure compared to the anchors without the PRs. The significant finding was in the failure mode, where severe concrete damage and concrete breakout failures were prevented by the PRs. The internal tensile stress of concrete was concentrated around the wedges of the anchors (interlocked area). The contribution of the PRs was shown by high strain values at around their mid-length. Additionally, due to the PRs, concrete cracking was less, mostly generated in the region between an anchor and its PRs. The utilization of PRs could be a method to protect concrete from breakout failure.

The buildup of corrosion products over a reinforcing bar and associated reduction in rib height lead to degradation of the bond between reinforcement and concrete. The authors have previously used digital image correlation (DIC) to visualize and quantify load-induced cracking at the interface in specimens with varying degrees of corrosion. The results obtained in that study are used here to simulate the post-corrosion local bond behavior. A bond degradation model is incorporated into the discrete analysis tool, 3D Rigid Body Spring Model (RBSM) for the simulation. This analysis method allows the shape of the reinforcing bar to be directly modeled, and concrete cracking behavior is simulated by using a randomly shaped mesh. The magnitude of opening and sliding over the tips of ribs in the simulation, in which the reduction in rib height could not be modeled, is significantly lower than observed in the experiment. The results demonstrate that reduction in rib height is an important factor in post-corrosion behavior, and needs to be included in simulation models. It is also understood that in order to gain a better understanding of local post-corrosion bond behavior, de-bonding between reinforcement and concrete needs to be modeled in a discrete analysis framework. [ABSTRACT FROM AUTHOR]

The 3D Rigid Body Spring Model (RBSM) is capable of simulating crack initiation and propagation in reinforced concrete under loading, providing otherwise elusive data on internal concrete cracks. This study introduces a comprehensive computational framework designed to simulate moisture transport in reinforced concrete under various damage conditions by coupling this simulation method with a proposed 3D RBSM conduit model. This enables crack formation and moisture transport in concrete to be simulated from a three-dimensional perspective. The conduit model places moisture pathways, or conduits, within RBSM elements to simulate moisture movement. Detailed parameters for humidity and crack characteristics are included, allowing for precise modeling of humidity distribution changes. First, the model's effectiveness is validated by simulating moisture transport in split-damaged concrete specimens and comparing the results with experiments. Subsequently, the validated simulation system is employed to simulate moisture transport in reinforced concrete beams under flexural conditions, considering the influence of the interfacial transition zone (ITZ) between steel and concrete and cracks on moisture transport. This accurately captures the moisture distribution within the model. This model facilitates a comprehensive understanding of the entire process, from predicting the development of cracks in concrete to moisture penetration in the cracked concrete, providing insights into the behavior of moisture under various concrete damage conditions. • 3D RBSM Conduit model simulates damage and penetration in reinforced concrete, combining mechanical aspects. • The model controls conduit equations, integrating effects of cracks, steel, ITZ, and concrete on moisture transport. • Practical 3D visualization accurately shows the model, cracks, and moisture distribution for clear representation. [ABSTRACT FROM AUTHOR]

The buildup of corrosion products over a reinforcing bar and associated reduction in rib height lead to degradation of the bond between reinforcement and concrete. The authors have previously used digital image correlation (DIC) to visualize and quantify load-induced cracking at the interface in specimens with varying degrees of corrosion. The results obtained in that study are used here to simulate the post-corrosion local bond behavior. A bond degradation model is incorporated into the discrete analysis tool, 3D Rigid Body Spring Model (RBSM) for the simulation. This analysis method allows the shape of the reinforcing bar to be directly modeled, and concrete cracking behavior is simulated by using a randomly shaped mesh. The magnitude of opening and sliding over the tips of ribs in the simulation, in which the reduction in rib height could not be modeled, is significantly lower than observed in the experiment. The results demonstrate that reduction in rib height is an important factor in post-corrosion behavior, and needs to be included in simulation models. It is also understood that in order to gain a better understanding of local post-corrosion bond behavior, de-bonding between reinforcement and concrete needs to be modeled in a discrete analysis framework.

The fracture process of dried concrete under splitting tensile loading was investigated using a three-phase mesoscale rigid-body spring model (RBSM). Although many studies have reported changes in the splitting tensile strength (f t) owing to drying, the mechanism remains unclear. The f t values under different drying conditions were predicted using a mesoscale concrete model that accounted for the drying-induced mechanical property change (DMPC) of mortar and microcracking. This result supports the assumption that DMPC and microcracking predominantly affect the strength under long-term drying. An investigation of the fracture behavior showed that drying-induced microcracking degraded f t by uniformly reducing the load-bearing capacity of the mortar. However, the cracks also had a slightly positive effect on f t by spreading the fracture area near the peak load, but this benefit was outweighed by the negative effect of cracking at 80 % RH or more intense drying conditions. • Microcrack-evaluation is a key to predicting tensile strength (ft) after drying. • Drying-induced microcracking is key for predicting the change in f t. • Considering creep behavior influenced an 8% change of calculated f t. [ABSTRACT FROM AUTHOR]

The seismic response of a medieval church in Central Italy is analyzed considering the two roof configurations, i.e., reinforced concrete and timber roofs, that the church had in different periods of its existence. Structural interventions and changes are common in the churches of this territory, where frequent earthquakes put these buildings at risk. The church studied here, St. Salvatore in Acquapagana (Serravalle di Chienti, province of Macerata), was damaged by the 1997 Umbria-Marche and the 2016 Central Italy earthquakes. Between these two seismic events, the church was repaired, and the concrete roof was substituted with a lighter timber roof. To investigate the influence of this change on the seismic response, a study was performed at the building and façade macroelement scales using the finite element model and rigid body spring model, respectively. For each approach, the two roof configurations were considered, and two strong motion records, from September 26, 1997, and October 30, 2016, were applied. The results show that the concrete roof improves the box-like behavior, but it increases the vulnerability of the masonry structures, characterized by a limited tensile strength. Conversely, in the timber roof configuration, the most vulnerable areas of the structure are the intersections between structural elements. [ABSTRACT FROM AUTHOR]

The development of artillery in Europe at the end of the Middle Ages brought a necessary change in military architecture. This change was a radical rethinking of the entire geometry and architectural design of city walls which required an increase in thickness to resist repeated artillery strikes. The damage due to the impact loads on Middle Age fortification walls is analyzed herein with explicit dynamic analyses. This study was developed both with finite element models and an innovative rigid body-spring model with diagonal springs (RBSM), showing the different peculiarities of these two different approaches and how their results can be integrated. The numerical models clearly showed that the presence of an inner core of softer material tends to modify the impact effects by reducing the degree of damage at the expense of an extension of the damaged area.

A new element based on the concept of Rigid Body Spring Model (RBSM) that inherently incorporates Poisson effect is developed and utilized to simulate the nonlinear behavior of concrete. Initially, the behavior of element in linear state is successfully verified. For the nonlinear applications in simulation of concrete, nonlinear material models are implemented based on mesoscale modeling technique that does not suffer from complexity of macroscopic models based on volumetric and deviatoric stress and strain tensors separation. Beside capability of incorporating the Poisson's ratio of the material, with the new material models implemented, the new element can represent the complex behavior of concrete. The uniaxial compressive and tensile test beside splitting tensile test on concrete specimen were simulated successfully and similar cracking patterns to the experiments were observed in the simulations. [ABSTRACT FROM AUTHOR]

• Long-term performance of massive RC structures was investigated by RBSM. • Deterioration is caused by cracks and mechanical property changes of concrete. • Impact of the whole history of massive RC structures was evaluated. • Impact on structural performance was clarified by altered seismic performances. • Impact on durability was examined based on crack distribution. Aging management and maintenance are essential processes to ensure the safety of reinforced concrete (RC) buildings in nuclear power plants (NPPs). This is because several phenomena induce cracking behavior and mechanical property changes (MPC) in concrete that might change the structural performance and durability of massive RC structures. Although massive RC structures have not been encountered with excessive loading or severe environmental conditions, structural performance and durability have changed owing to cracks regarding restraint volumetric changes (e.g., thermal and drying-shrinkage cracks) and MPC of concrete throughout the service life. This study numerically investigated the whole history of massive RC structures observed under the general conditions of NPPs in Japan. The alternation in seismic performance according to the whole history of the structure was investigated using a rigid body-spring model. The impacts of restrained cracks, the interaction with structural cracks, and the MPC of concrete were determined to clarify their significance, which is generally neglected for the design and inspection process in the engineering practice. [ABSTRACT FROM AUTHOR]

• Rigid body spring model, which can simulate the effect of drying on the RC structure, was developed. • The proposed numerical model reproduced RC beam loading test results. • Modeling of the dowel effect of reinforced bars needs further study. To improve the aging management of nuclear power plants (NPPs) and to extend the plant life by allowing long-term operation, a numerical model, which can evaluate the changes in the structural performance due to drying (i.e., drying shrinkage, resultant shrinkage-induced cracks, and property changes due to desiccation), is proposed. For the numerical model, a 3D rigid-body-spring-network model (RBSM) combined with a truss network model was adopted, and moisture transport, subsequent drying shrinkage, and changes in physical properties were implemented. In this study, four beams were analyzed, with two beam sizes without stirrups being subjected and not subjected to desiccation, respectively. All beams considered for the numerical investigation are shear critical. The numerical model produced reasonable results for the following points: 1) a strain distribution of rebar after drying, 2) changes in diagonal cracking patterns, and 3) trends in the load–deformation relationship, especially with the diagonal-cracking strength showing agreement with the experimental result. However, the ultimate shear strengths did not correspond with the experimental results. Based on previous research, this discrepancy can be improved by considering the "dowel effect" at the shear failure. [ABSTRACT FROM AUTHOR]

A newly developed coupled numerical model is presented to investigate the compressive localization and softening behavior of concrete under steel tube confinement. The coupled model combines the use of rigid body spring model (RBSM) and nonlinear shell finite element method (FEM) to simulate concrete and steel in steel tube–confined concrete members. Numerical evaluation of compression localization in steel tube–confined concrete columns showed that the compressive behavior of this type of column is also localized and that the length of compressive fracture zone was found to be more localized in square cross section than equivalent circular cross section. With increasing slenderness and level of confinement, it was found that localization length increases with increasing confinement, and for higher confinement level, localization zone can only be observed in longer specimens. This means that localization and softening of concrete can always occur irrespective of confinement level but depends on the size (height) of the member. [ABSTRACT FROM AUTHOR]

Frost damage is an important issue for service life evaluation of concrete structures in cold regions. In fact, the frost action can have both strengthening and damaging effects on the mechanical properties of concrete material, depending on several environmental and material factors, and this complexity makes the damage evaluation more difficult in the real environment. This paper aims to develop a unified model through a micro‐mesoscale approach, which can quantitatively estimate and distinguish the strengthening/damaging effects by frost action. At microscale, the model takes into account the prestressed condition by internal pore pressures, as well as the change of effective elastic properties when ice forms in micropores. At mesoscale, the mechanical contribution of ice and liquid inside mesocracks is considered. Finally, the static mechanical behaviors of concrete under different situations are simulated based on a two‐dimensional discrete model rigid body spring method. The simulated results can clearly distinguish and separate each strengthening and damaging effect. The microice may enlarge the strengths by 50–110% while the mesocracks may reduce the strength by 40–80%, the effect of ice in mesocracks is also discussed. The final apparent performance depends on which strengthening/damaging effect is more dominant and is mainly controlled by the entrained air amount. Previous experiments are also used to verify the proposed model, and they are found in a good agreement. [ABSTRACT FROM AUTHOR]

The failure of a laminated glass beam is investigated by two full discrete numerical approaches: a Rigid Body-Spring Model (RBSM) and a mesh-free numerical method arising from bond-based Peridynamics (PD). The brittle nature of the failure has been modelled and investigated by exploiting the discrete nature of these models, and specifically the PD which allows the bond/spring strengths to be explicitly related with the size and orientation of the defects in the structure. Strength values have been assigned randomly, within the beam, by a Monte Carlo simulation, according to Weibull statistical distributions calibrated on experimental results obtained from literature. For the first time, the differences and analogies of the two discrete approaches are shown and discussed together with the analysis of variability of the load capacity of the beam related to the statistical presence of flaws in the structure. Results show that, due to the heterogeneous strength properties of the numerical models and mechanical features of the inter-layer, multiple cracking stages can be distinguished for the structural element, thus different cumulative distribution function of limit load can be obtained. [ABSTRACT FROM AUTHOR]

By employing the improved rigid block spring method, the failure process of a sandstone example containing a single open fissure under uniaxial compression is modelled. In this method, the intact rock is considered as an assemblage of rigid polygonal blocks. Macro mechanical behaviours are governed by mechanical properties of interfaces between two neighbouring blocks. In the local scale on interfaces, both tensile splitting failure and shearing sliding failure are considered. Micro properties are obtained by a calibration procedure against the stress-strain curve of intact rock under uniaxial compression in the lab. Influences of fissure inclination and length on the uniaxial compression strength (UCS) and failure modes are discussed. Comparisons between numerical simulations and laboratory tests are presented. The growth process of micro-cracks is studied and the mechanism of micro-crack propagation is studied through analysis on the displacement evolution. Some conclusions are drawn: numerical results generally agree well with those from lab tests; the UCS of fissured rock is lower than the intact one; the UCS first goes down then goes up as inclination increases, but decreases gradually as fissure length increases; the micro failure modes are governed mainly by tensile splitting failures. [ABSTRACT FROM AUTHOR]

A two-dimensional molecular model is presented for the elastic non-linear modelling and design of meta-materials. The fundamental unit-cell, based on a heuristic molecule (HM) approach, is composed of atoms that interact through centred and non-centred spring-based bonds. The kinematics formulation allows to consider large displacements and finite strains while the specific topology of the HM can be parametrized to modify the shape of the rigid atoms and the size of the bonds. The HM is frame indifferent and provides a remarkable quasi-isotropic elastic response for both deviatoric and volumetric large deformation modes. At a macro-scale, the relationship with different continuum materials is given through a standard isotropic Cauchy up to an isotropic Cosserat solid. Evidence on the interest of the model as a calculation tool is provided by studying the elastic response of standard and auxetic materials subjected to a non-homogeneous deformation field, as well as the response of auxetic foams under large deformations. Aside the numerical agreement, it is highlighted how the tailoring of the HM topology can be effective to approximate the non-linear geometric effects that occur at finer scales of auxetic foams. In perspective, we address how the exotic mechanical properties provided by the HM, together with the assumed physical-driven framework, can foster the engineering application and the design of new meta-materials. [Display omitted] • 2D molecular model for the elastic non-linear modelling and design of metamaterials. • Heuristic molecule (HM) composed of atoms that interact through spring-based bonds. • The kinematics of the HM allows to consider large displacements and finite strains. • The geometry of the HM is parametrized to design different topologies • The HM features a remarkable elastic quasi-isotropy under large deformations. • HM as a calculation tool is evidenced for the study of standard and auxetic materials. [ABSTRACT FROM AUTHOR]

A numerical investigation on the load carrying capacity of a laminated glass beam modelled as a material with a random strength distribution is presented. The strength values were distributed randomly within the beam by a Monte Carlo simulation, according to statistical distributions calibrated on experimental results obtained from literature. A preliminary computational analysis based on the weakest link in the chain-model was conducted to study the dependence of the beam estimated limit load on the adopted discretization. Then, after determining the optimal size of the mesh, the elastic-plastic problem has been solved by a Rigid Body-Spring Model (RBSM) discrete approach. Finally, the variability of the load capacity of the structural element is evaluated as a function of the statistics of the strength related to the size of the defects. One thousand simulations were performed to obtain statistically significant quantitative results. [ABSTRACT FROM AUTHOR]

Study of the wrist kinetics is important role in progressive of pathology and researches hope to develop new therapies for reduce the pains and restore the functional ability in the wrist joint. The aim of this study is investigating and comparing the peak contact pressure in radio-scaphoid articular joint with regard to finite element method & Rigid Body Spring Model method. With RBSM technique the structure of the wrist is represented in a model as a collection of rigid bodies, representing the bones, interconnected by compressive and tensile spring elements, representing cartilage and ligaments. This Method includes mathematical formula that calculated the stress & strain in regard to impact load in the Radio-Scaphoid joint. Results for joint model indicate that these two methods predict similar peak contact pressure on joint surface. But the RBSM is relatively simple and effective in predicting joint contact pressure under symmetric and non-symmetric loading. The computational efficiency of the RBSM method is particularly attractive for pre-operative planning of reconstructive surgical procedures in orthopedics.

• Thermal cracking on massive reinforced concrete (RC) member was quantitatively evaluated. • Newly proposed constitutive laws on the 3D-RBSM were proposed for this objective. • Crack width and crack spacing of massive RC walls subjected to external restraint were evaluated. • Time-dependent cracking behavior of a massive RC wall structure was clarified. • Impacts of factors affecting thermal cracking were studied using the proposed method. This study aimed to develop a numerical method to evaluate thermal cracking, in terms of parameters such as thermal crack width and crack spacing, on massive reinforced concrete (RC) wall structures externally restrained by a base structure. The existing experimental study was investigated using the rigid body–spring model (RBSM) with new constitutive laws developed for this objective. Thermal cracks, which localized and propagated throughout the wall thickness, were successfully reproduced, and the good agreement with the experiment indicated the capability of the proposed numerical method. The time-dependent cracking behavior and the impacts of factors affecting thermal cracking, which are difficult to investigate experimentally, are discussed. [ABSTRACT FROM AUTHOR]

Frost damage is one of the most important deterioration factors for porous materials in cold and wet region. In this study, a mesoscale numerical study is conducted to estimate the frost damage of rock materials based on the Rigid Body Spring Method. The mesoscale elastoplastic constitutive law is presented cooperated with the ice formation model for the rock material. Then, the cyclic expansion of selected marble during multiple freeze-thaw cycles (FTC) is simulated, resulting in different values of residual strain. It is found that using the residual strain as a link between freezing process and mechanical degradation, the damaged compressive behaviors after different numbers of FTC can be successfully explained and reproduced, including the crack recovery phenomenon. The findings in this study are beneficial for the further simulation of frost deterioration history, considering the large variability in properties of rock material. • The mesoscale elastoplastic constitutive law is presented cooperated with the ice formation model for the rock material. • Compressive performance of marble afterFTC is evaluated by mesoscale analytical approach with a discrete element method. • The residual strain is suggested as the damage index for rock materials suffering frost damage. • An empirical model to predict the frost-damaged compressive behaviors with residual strain is developed for application. [ABSTRACT FROM AUTHOR]

The rigid bodies-spring model (RBSM) has been developed as a numerical model to generalize limit analysis in plasticity, in which the structure to be analyzed is idealized as an assemblage of rigid bodies connected by normal and tangential springs. Originally, this approach was a discrete model for handling static problem. In this paper, we illustrate the formulation of an explicit dynamic method for each element using the principle of hybrid-type virtual work. Additionally, we propose a new RBSM approach for contact mechanism and friction characteristics. Finally, we verify the accuracy of dynamic analysis by RBSM with some numerical examples. [ABSTRACT FROM AUTHOR]

This work is devoted to numerical analysis of permeability in rocks with multiple fractures. We propose a discrete approach for porous media with dual porosity. The intact porous rock is first discretized by an assembly of impermeable blocks according to the Voronoi diagram. The pore space of the intact rock is replaced by an equivalent network of interfaces between blocks, which produces the same macroscopic hydraulic conductivity as the intact rock. An induced network of macroscopic fracture or cracks is then introduced into the discrete porous rock. A specific numerical algorithm is developed to solve the obtained dual-porosity discrete porous medium. A series of numerical studies are performed in order to verify the efficiency of the proposed method and to investigate influences of mesh sensitivity, effects of fracture geometry and distribution. The proposed model is then applied to the study of permeability evolution in rock samples submitted to biaxial compression tests with different confining pressures. It is found that the proposed model is able to correctly reproduce the progressive process of initiation and propagation of fractures and the related evolution of permeability. [ABSTRACT FROM AUTHOR]

• Discrete modeling can directly simulate corrosion-induced bond degradation. • Corrosion damages cause loss of tension stiffening effect. • Occurrence of corrosion increases widths of load-induced craoor bond condition reduces the stress transfer from reinforcement to concrete. • Internal stress conditions during uniaxial tensile loading were visualized. Corrosion-induced bond degradation leads to changes in deformation characteristics, cracking patterns, and loss in tension stiffening in structural members. Since the induced damage is dependent upon multiple inter-related parameters, prediction of post-corrosion deformation behavior requires sophisticated numerical simulations. This study integrates corrosion expansion and bond degradation models into a discrete analysis framework, 3D RBSM (Rigid Body Spring Model), to simulate post-corrosion loss of tension stiffening. Uniaxial tensile loading is applied to reinforced concrete models with different degrees of corrosion to obtain plots of load versus average strain and surface cracking patterns. Simulated surface cracking patterns due to corrosion and uniaxial loading in uncorroded and corroded models are similar to experimental results. As the degree of corrosion increases, the number of transverse cracks on the concrete surface decrease and the load at first cracking also decreases. Further, internal stress and bond stress investigation directly illustrate the decrease in stress transfer from reinforcing bar to concrete due to corrosion. [ABSTRACT FROM AUTHOR]

Nowadays, seismic design code in Japan is becoming more stringent. To satisfy the strict requirement, larger numbers of reinforcements must be placed, resulting in increased reinforcement congestion. To reduce the reinforcement congestion, mechanical anchorage is becoming popular in use instead of conventional hook rebar. However the behavior of mechanical anchorage placed in thin cover zone is not well understood, and the use of this is still limited. In this study, the discrete element method was used to investigate the performance of mechanical anchorage placed in thin cover depth zone, and the pull-out test in previous research was simulated. To assume that anchor plates welded to bar end are difficult to place side by side due to closely-spaced reinforcements, the position of anchor plate was taken as main parameter. The result shows that the anchorage performance changed according to the transverse bars effect and the shift of the mechanical anchorage. The simulations show good agreement with experiment data in terms of the anchorage capacity, crack pattern and failure mode. [ABSTRACT FROM AUTHOR]

• Investigating the interaction of multiple corroded rebars and its effect on corrosion cracking. • Non-uniform experimental corrosion and ideal uniform corrosion profiles are considered. • The relationship between rebar corrosion and surface crack width is not unique in multiple corroded rebars. • A crack generated by corrosion can close when the location and order of corrosion rebars change. In real structures, corrosion cracking patterns tend to be complex as a result of congested rebar arrangements and non-uniform corrosion distribution. It is challenging to understand the internal corrosion cracking behaviour based only on the limited amount of visible surface cracks. The present study attempts to use a meso-scale discrete element method, the three-dimensional rigid body spring model (3D-RBSM), to simulate factors that affect corrosion cracking. Factors considered in reinforced concrete panels with multiple corroded rebar includes, corroded rebar location, corrosion order among rebars and rebar arrangement. Three different cases are simulated and the results are compared with previously published experimental results. In one set of simulations, the non-uniform rebar corrosion profiles obtained in the experiments are utilized, with the results showing similar cracking patterns to the experimental ones. In a second set of simulations, uniform corrosion is assumed so as to conduct a parametric study of the same specimens for an accurate understanding of each influencing factor. It is observed that when all rebars corrode simultaneously, the initial cracks propagate along the outer rebars because this is where the confinement effect is minimum. Cracking along inner rebars is delayed due to strong compression zone resulting from mechanical interaction among corroded rebar stresses. However, this compression zone is reduced when the rebars corrode in two stages and cracking occurs at all the rebar locations. Cracks that initially form along the inner rebars can close up when corrosion of the outer rebars occurs later. [ABSTRACT FROM AUTHOR]

SUMMARY The paper proposes a systematic comparison between two methods of analysis that are well established in the field of earthquake engineering: nonlinear dynamic analysis and nonlinear static procedure (NSP), applied to the out-of-plane seismic response of two masonry façades representative of many ancient Italian churches. The comparison is based on extensive numerical analyses, which focus on the flexural and torsional mechanisms, while the in-plane damage mechanisms and the possible detachment between the façade and the lateral walls because of a poor connection have been presently disregarded. The computations, both in the static and in the dynamic field, are based on a rigid body and spring model specifically implemented for this issue, computationally efficient and equipped with a realistic model of damage and hysteresis at the mesoscale. An innovative aspect of this study is the heuristic modelling of three-wythe masonry, to include some typical texture effects on the macroscale nonlinear response. For each façade, two different masonry textures were considered, performing extensive dynamic analyses that offered a detailed overview about the performance under earthquakes of different intensities. In parallel, NSP and the classical N2-based seismic assessment were applied. A critical discussion and comparison of the results of the two methods is presented to rationally appraise limits and opportunities. In particular, flexural and twisting out-of-plane mechanisms were clearly appraised in the dynamic field, whereas NSPs were not always able to describe the collapse, because they missed the partial failures determined by higher vibration modes, as could be expected. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The seismic analysis of a large monument subjected to strong earthquakes is the object of the present paper. As a case study, the response of the “Maniace Castle” of Syracuse has been investigated by a multi-level approach which adopts traditional finite element modelling as well as a specific mechanistic computational model for the final non-linear seismic analyses. At first, the linear behaviour of the monument was studied by means of two 3D FE models in order to understand the global response of the building, its points of weakness, and the kinematics of the corresponding collapse mechanisms. Then, these results were used to calibrate a mechanistic 2D plane rigid body and spring model, RBSM, specifically formulated with the aim of approximating the macroscopic behaviour of masonry walls with reduced degrees of freedom, and taking into account the influence of the masonry texture and energy dissipation capacity of the material. Given the uncertainties and the variability of the material characteristics, an extensive parametric non-linear static analysis and the dynamic analyses, with artificial and natural accelerograms, were made in accord with the EC8 seismic code, and compared together. These results were then used to formulate and verify a simple proposal for the restoration design. [Copyright &y& Elsevier]

The development of artillery in Europe at the end of the Middle Ages brought a necessary change in military architecture. This change was a radical rethinking of the entire geometry and architectural design of city walls which required an increase in thickness to resist repeated artillery strikes. The damage due to the impact loads on Middle Age fortification walls is analyzed herein with explicit dynamic analyses. This study was developed both with finite element models and an innovative rigid body-spring model with diagonal springs (RBSM), showing the different peculiarities of these two different approaches and how their results can be integrated. The numerical models clearly showed that the presence of an inner core of softer material tends to modify the impact effects by reducing the degree of damage at the expense of an extension of the damaged area. [ABSTRACT FROM AUTHOR]

A discrete Lagrangian approach is the basis for modelling the macroscale elastic response of a solid material, which can be homogeneous as well as a periodic composite. The basic topology is a square "heuristic molecule" that is an assemblage of four rigid bodies with a definite shape bonded by elastic springs. This is the minimum unit cell, UC, that contains all the macroscopic mechanical properties of the solid material, object of study. The paper presents 4 unit cells, in progression from a basic molecule bonded by 2 types of central forces, to a refined "Cosserat-auxetic" molecule that is connected by 4 types of shear and central bond-springs. The emphasis is given to the isotropic response in relation to the value of the macroscopic Poisson ratio, and the four examples of UC topologies are presented showing their relationship to different materials at the macro-scale: from a "rari-constant" continuum, through a standard isotropic Cauchy continuum, up to an isotropic centre-symmetric auxetic Cosserat solid. [ABSTRACT FROM AUTHOR]

The confining effect of concrete cover and stirrups reduces the rate of bond deterioration due to corrosion. However, the large dispersion in recorded experimental data makes it difficult to clearly separate the influence of cover depth and stirrup confinement on bond degradation. This study utilises the discrete 3D Rigid Body Spring Model (RBSM) to conduct a meso-scale investigation regarding the effect of cover thickness and stirrup confinement on internal crack evolution and pull-out behaviour in corroded reinforced concrete models. The simulation scheme is divided into two stages. In stage 1, different degrees of corrosion are introduced, producing cracking in the cover concrete; in stage 2, the corroded main reinforcement is pulled out from the damaged concrete. 3D RBSM is advantageous because the concrete is randomly meshed to reduce mesh bias on crack propagation and the actual geometry of the deformed bars is modelled. The simulation results clarify that the presence of thicker cover delays crack initiation but increases the rate of crack opening. Stirrups do not have any significant effect on crack initiation but effectively restrict crack growth. An investigation of the internal stress in the simulation models shows that tensile stresses generated in stirrups during corrosion are responsible for reactionary confining pressure that restricts crack propagation. Load-displacement curves show reductions in pull-out capacity, stiffness and ductility with increasing corrosion damage. The relative influence of crack opening and stirrup volume on the rate of bond degradation with respect to average surface crack width are discussed and compared with published experimental results and an empirical equation. [ABSTRACT FROM AUTHOR]

• Rigid Body Coupled Spring discrete element was extended to simulate fibrous concrete. • cases of tensile, flexural, compression and push-off shear tests were simulated. • fibre pull-out action in meso -scale was not enough create compressive behaviour. • load-crack mouth opening curve of 3-point bending models is comparable to experiment. • fracture patterns in push-off simulation are similar to the experimental results. As a complementary part of a previously developed discrete model, Rigid Body Coupled Spring (RBCS), the model is extended to simulate and predict the behaviour of Steel Fibre Reinforced Concrete (SFRC) by modifying mesoscopic shear material model and introducing fibre contribution to mesoscopic tensile material model with respect to the inclined fibre pull-out behaviour. Several types of rounded-straight steel fibre with various volume fractions were used in these simulations and the outcome was compared with related experimental studies. Studied cases include uniaxial compressive behaviour, direct tension behaviour, flexural and direct shear behaviour. The results have confirmed the success of this approach in the studied cases. [ABSTRACT FROM AUTHOR]

• RBSM simulation agrees with the experimental results. • Post-installed reinforcement aid anchors to resist higher pull-out force. • Post-installed reinforcement reduces displacement of anchors at specific loads. • Cracks in vicinity of anchor are suppressed by post-installed reinforcement. • More concrete elements near anchor are in compression due to post-installed reinforcement. The utilization of post-installed anchors is growing fast to connect both structural and non-structural members. Adhesive anchors are one type of post-installed anchors which are formed as threaded bars. They can be post-placed into concrete with the help of epoxy adhesive. On the one hand, improvement of the performance of post-installed anchors, unlike cast-in-place anchors, has not drawn attention much. On the other hand, due to the complexity of their performance, a numerical study can be a supportive method for the experimental study. This paper addresses the effect of post-installed reinforcement (PR) on the adhesive anchors under tensile loading in both experimental and numerical studies. Reinforcing steel bars as post-installed reinforcement (fully embedded in concrete) were used to ameliorate the performance of the adhesive anchors under tensile force. Rigid Body Spring Model (RBSM) was developed as a simulation that is based on discrete analysis at mesoscale. Pull-out capacity, displacement, failure mode, and concrete cone geometry were measured by the experiments and the RBSM simulation. In addition, internal stress, strain, cracking patterns were investigated by the RBSM simulation. Moreover, some comparisons were conducted through the existing standard. In general, PR assist the anchors to have higher pull-out capacities, lower displacement as well as leading smaller size of concrete cone failure. Due to PR, the internal tensile stress of concrete changed to compressive stress resisting greater pull-out force. The higher strain is obtained at near the top of the anchors and at the mid-span of PR. Furthermore, cracking patterns in concrete were mostly within the area between the anchor and PR. Post-installed reinforcement can be considered as a method to improve the performance of adhesive anchors under tensile loading. This is validated by the RBSM simulation, which agrees with the experimental results. [ABSTRACT FROM AUTHOR]

• Even surface cracking conditions are similar, internal stress and cracking vary greatly. • Strength and stiffness can increase with expansion in case of coupled damage. • Internal cracking and stiffness are important to estimate structural performance. Real concrete structures can suffer simultaneously from the alkali-silica reaction (ASR) and delayed ettringite formation (DEF), resulting in expansion of the concrete and surface map cracking. This damage can lead to serious durability problems. The respective effects of ASR and DEF have been studied, but the cracking behavior of concrete when they act together remains unclear. In this study, a three-dimensional rigid body spring model (3D RBSM) is used to simulate the cracking and mechanical property degradation of concrete under coupled ASR and DEF. A parametric study is conducted to understand various combinations of ASR and DEF. In line with previous studies by the authors on independent ASR/DEF damage, expansions caused by ASR and DEF are, respectively, introduced as strains at the mortar-aggregate interface and in mortar elements. Due to a confinement effect, specimens subjected to coupled expansion may suffer less expansion or cracking than when only one of the degradations is acting. The model clearly visualizes the cracking process and stress development as the degree of coupled expansion increases. More importantly, based on the simulated results, the interactions of the two types of expansion are revealed by correlating the degradation in mechanical properties with internal cracking behavior. Further, the confinement effect arising on application of the second type of expansion is quantitatively examined. While there is no significant change in stiffness, compressive strength in some cases increases with expansion as larger cracks close up under the confinement effect. This kind of investigation of coupled effects is difficult to quantitatively analyze through experimentation, but this work demonstrates that it is possible using RBSM simulations. [ABSTRACT FROM AUTHOR]

• Effects of concrete cracking on corrosion damage are isolated and analyzed by using an innovative pull-out test. • Effect of corrosion is modeled by adjusting springs at the corroded interface in the RBSM-based simulation. • RBSM simulation can visualize internal stress development as the degree of rebar corrosion increases. Rebar corrosion can lead to significant deterioration in bond strength between steel and concrete. However, since confinement is lost as the concrete cracks, the changes in frictional bonding and mechanical bonding resulting from corrosion remain unclear and there is a need for an efficient tool that can evaluate the bond performance of corroded concrete structures. In this study, an innovative pull-out test is used to study changes in bonding in reinforced concrete after rebar corrosion, then a discrete meso-scale model based on the Rigid Body Spring Model (RBSM) is developed to simulate the observed bond behavior. To isolate the effects of concrete cracking, after an initial pull-out test, the corroded rebars are obtained and used as the reinforcement in newly cast sound specimens that are subject to a further pull-out test. A corrosion acceleration method is used to obtain corroded rebars. Different types of reinforcement (round rebars and deformed rebars) are studied. The results are used to study changes in frictional bonding and mechanical bonding at different degrees of corrosion. It is found that, without concrete cracking, the frictional bond in specimens with both round and deformed rebars significantly increases with the amount of corrosion, while total bond strength of specimens with deformed bar is almost unchanged because mechanical bonding is weakened. In the presence of concrete cracking, for specimens reinforced with a corroded round rebar, bond capacity increases initially (up to 3% corrosion) and then falls as corrosion increases, while bonding in those with a corroded deformed rebar shows a consistent decrease. In the RBSM-based simulations, the effect of corrosion is modeled by adjusting springs at the corroded interface. Constitutive models of shear and normal springs are developed to simulate corrosion and reflect the changes on frictional and mechanical bonding. Simulated results for load-displacement relationship, pull-out capacity and crack pattern are in good agreement with the experimental results. The numerical simulation is used to visualize internal stress development and strain distribution along the rebar as the degree of corrosion increases, a result that cannot be obtained by experimental methods. The results demonstrate that RBSM is a useful tool for evaluating the mechanical performance of corroded reinforced concrete structures. [ABSTRACT FROM AUTHOR]