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![Figure 10: fracture energy based regularization in 2-scale FEM [41]](profile/Luca-Pela/publication/309882050/figure/fig10/AS:668253294690307@1536335409102/fracture-energy-based-regularization-in-2-scale-FEM-41_Q320.jpg)
![Figure 11: Tested wall geometry and obtained failure pattern [47]](profile/Luca-Pela/publication/309882050/figure/fig2/AS:427995732156421@1479053542878/Tested-wall-geometry-and-obtained-failure-pattern-47_Q320.jpg)
This work presents a multiscale method based on computational homogenization for the analysis of general heterogeneous thick shell structures, with special focus on periodic brick-masonry walls. The proposed method is designed for the analysis of shells whose micro-structure is heterogeneous in the in-plane directions, but initially homogeneous in...
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In this paper, a novel adaptive multiscale model is proposed for accurately predicting the nonlinear mechanical response of periodic brick masonry due to crack initiation and propagation under general in-plane loading histories. Such a model relies on a two-level domain decomposition technique, used in conjunction with an adaptive strategy able to...
The research reported herein involved constructing and shake-table testing two quarter-scale models of an as-built and retrofitted two-storey brick unreinforced masonry (URM) building. The tested buildings were based on a prototypical, lower bound, two-storey row building with a parapet roof and typical shop front openings. Recycled vintage clay br...
Masonry is one the most employed building materials, and there is a large population of existing and historical unreinforced masonry (URM) constructions in earthquake prone re- gions all over the world. The lateral capacity of shear walls significantly affects the overall behaviour of both unreinforced and masonry-infilled RC frame buildings. Howev...
Citations
... The framework of the multi-layer shell element: a material classes and b overall procedure for defining the multi-layer shell element , modified by (Al-Ahmar, 2022) These conditions are achieved with the Heaviside function H(x). The inactive parts of the two surfaces, that is, the parts cut out by the Heaviside function, are plotted in transparency in Fig. 5 (Petracca et al., 2017b). ...
To simulate the realistic nonlinear behavior of reinforced concrete shear walls, which are an efficient structural system for resisting lateral forces, it is crucial to choose the appropriate numerical models and constitutive materials. Because of this, the current research, through two research portions, examines the seismic response of RC shear walls using a combined model of a multi-layer shell element and fiber beam element. This combined model of RC shear walls is guaranteed to be used in sequential and parallel analyses by comparing the results of using several model types of concrete’s nonlinear materials and shell elements. First, this combined model is used to calibrate the hysteretic curve resulting from the experiment of an RC shear wall subjected to a cyclic load. Second, the seismic response of RC shear walls in a building, with critical dimensions and numbers of shear walls, designed according to the Syrian Arab Code and subjected to a strong earthquake is assessed. The analysis’s findings demonstrate that the combined model of the RC shear wall and the experimental data from the hysteretic curve calibration agree well. It also notes that the performance level of the studied building, for all material types, reached collapse and collapse prevention levels according to damage and story drift ratio approaches, respectively, indicating that the shear walls’ design using the equivalent static method is unsafe for this studied building. This emphasizes the necessity of using sophisticated nonlinear models of materials and elements along with performance-based seismic design to develop the shear walls’ actual behavior.
... Feyel [21] developed a two-level finite element method (FE 2 ) for calculating complex structures, combining multiscale finite elements and parallel computation. Mercatoris et al. [22] and Petracca et al. [23] proposed two-scale homogenization schemes for the thin and thick shell-like masonry walls, respectively. ...
... To this end, a novel damage-mechanics-based continuous micro-model was employed. This model is based on the "tension/compression (d + /d − )" damage model [40][41][42] which can capture the nonlinear shear behavior of masonry walls as well as control the effect of dilatancy. In this model, the effective tensor of stress (σ eff ) is defined by the bi-dissipative damage model: ...
... d + and d − are the tension and compression damage indices for the inelastic part of the effective stress tensor, correspondingly. For the failure criteria, two scalar measures of τ + and τ − (also called equivalent stresses) are employed [40][41][42]: ...
... This method is more flexible than the conventional ones [42]. For further information on the aforementioned damage model, the readers are introduced to ref. [40][41][42]. ...
This study presents a comprehensive investigation of the in-plane response of unreinforced masonry shear walls with regular openings, under the action of monotonic lateral displacement. Walls are considered with several pre-compression loads as well as different window and door openings configurations. To this end, a group of masonry shear walls built with clay bricks and hydraulic lime-sand mortar was selected featuring regular opening layouts. The micro-modeling approach was utilized by considering complex constitutive laws for materials' nonlinear behavior for capturing damages in elements. Results from the nonlinear analysis of the walls were obtained, including the lateral load capacity of shear walls at different performance points, their lateral displacement, stiffness, ductility capacity, normalized absorbed energy, and the overstrength, force reduction, and response modification factors. Moreover, a full discussion is presented regarding the estimating equations from the ASCE 41–17 code on the maximum shear capacity of the walls including their accuracy to predict the shear capacity of URM walls with openings. It is observed that opening reduces the shear strength of the unreinforced masonry shear wall between 5 and 60% as well as a reduction of 10–85% in its effective stiffness, depending on the intensity of the pre-compression load. Moreover, the code’s estimation equations for shear strength of unreinforced masonry shear walls lead to an underestimation. For walls with two or more openings of window or door, the average strength from the upper and lower bound of the code-based strength seems appropriate, considering an intense pre-compression load on the wall.
... Even though solid and shell elements can better represent the system geometry of masonry structures, dimensionally reduced 1D and spring elements are extensively used for seismic and blast simulations because of their optimized computational costs ( [11][12][13][14][15] for some seismic masonry examples). Continuum-based masonry macro models are typically accurate in the structural simulation (examples for in-plane loading include references [8,16] and out-of-plane loading [17][18][19][20]), however, estimating non-homogeneous material properties as unstructured bonds and detailed crack predictions is, up-to-date, complex. Apart from analytical and continuum based approaches, mesh free or particle based methods find increasing application in masonry classification as well (e.g. ...
... Within this section the continuum based d þ /d Àdamage model from [10,17,38] shall be discussed. The aim of this research is the modelling of thin walled masonry. ...
... The shear reduction parameter k 1 is introduced to control the compressive strength in the shear state, which properties are shown Fig. 1. Petracca [14] and Petracca et al. [17] provide comprehensive studies on the structural effect of this parameter. Finally, the factor k b is defined by the ratio from the biaxial strength of the applied material (see Fig. 1). ...
This research presents a constitutive model for the macro scale simulation of masonry structures. The model is containing an orthotropic plane stress assumption, which appears as an appropriate assumption for the in-plane analysis of masonry walls. The material model is based upon damage mechanics, split into tensile and compression parts. The novelty herewith is the consistent mapping of the damage evolution laws. Aim of this research is to develop a simple but accurate constitutive law, suitable to simulate large scale structures and buildings with reasonable computational costs. The developments are presented and compared with available literature examples from laboratory testings.
... [60,61] have introduced a model which achieves the orthotropic behavior by a mapping between directions, known from [58]. This mapping has been considered within [72], while relying on the damage evolution laws from [62][63][64]. Within the presented research, this constitutive model shall be considered for the aimed macroscopic assessments. The specifics shall not be repeated in detail within this scope. ...
... • Petracca et al. [62]: FE 2 multiscale model • Abdulla et al. [2]: simplified micro model • Noor-E-Khuda et al. [54]: explicit macro model • Noor-E-Khuda [53]: explicit macro model with continuum shell elements ...
... Petracca et al. [62] have simulated the half of the wall and have employed symmetry conditions. The proposed IGA avenue would bring the boundary shape functions within the spectrum of the measurements. ...
This publication presents a novel numerical avenue for the assessment of masonry structures. To circumvent the labor-intensive finite element method modeling and pre-processing step, the isogeometric analysis is enhanced within this contribution to cope with the necessities for masonry structures. This incorporates the study of apparent kinematic shell formulations, including their respective properties. Additionally, the connection towards non-linear material laws is outlined, and an empirically evaluated approach for the element size regularization is proposed. This generic approach would be inherently valid for other size dependent constitutive material models, as e.g. concrete models.
The current paper is explored in the context of a number of experimental problems. These validation examples are used to provide structural assessments that extend beyond the scope of the experiment. Finally, a potential example that provides an outlook towards anticipated applications is presented.
... The values considered for each mechanical parameter of the materials are presented in the section of the calibration of the models. The compressive (G c ) and the tensile (G t ) fracture energies have been computed according to the equations presented in Ref. [70]. These are automatically divided by the element characteristic length (l ch ) to obtain a response that is mesh-size independent. ...
... In this regard, the masonry is modelled as an isotropic or anisotropic homogeneous continuum (Degli Abbati et al. 2019). One of the most complex tasks in this type of modelling is to define the material's anisotropic inelastic behaviour (Petracca et al. 2017b). Employing a solid 3D Finite Element (FE), which represents the mechanical behaviour of the masonry in a continuous form, enables the maintenance of cost-effective computational efficiency (Tiberti et al. 2016). ...
... The failure criteria of this material model have been described in (Petracca et al. 2017b). In this regard, equivalent stresses τ + and τ-have been defined to identify the reciprocating loads conditions. ...
... stresses is positive. These conditions are implemented in the definition of each surface with the Heaviside function H (x) (Eqs. 2 and 3) (Petracca et al. 2017b). Furthermore, the tensile and the compressive surfaces might be active when the principal stresses have different signs. ...
Existing heritage buildings can be especially vulnerable to earthquakes. They were designed only considering gravity loads and some of them are located in earthquake prone areas, such as the southwestern Iberian Peninsula. Besides, there is a high uncertainty in the definition of their constructive parameters and complex geometry. Due to that, it is paramount to develop accurate numerical models to obtain a reliable assessment of their seismic behaviour. Given this, the main objective of this manuscript is to analyse the seismic behaviour of the Giralda tower, located in Seville (Spain). It was declared as a Word Heritage Site of Outstanding Universal Value by the UNESCO in 1987. Seville has a moderate seismic hazard, but it has been shown that the soft alluvial strata amplify the seismic action. The tower has a brick and stone masonry structure, which was constructed in several construction phases. A 3D Finite Element Model of the tower has been developed using OpenSees software, employing a 3D CAD model. Modal analyses and nonlinear static analyses have been applied to calibrate and to assess the tower’s seismic behaviour. The results showed significant differences in function of the load pattern. It should be remarked that the boundary conditions have a notable effect upon getting a good calibration of the model. Regarding the damage, it has been found to match the historic records: the ramps would be ruined and, in the outer wall, it would be concentrated near the openings, especially close to the belfry.
... These schemes are numerical frameworks that are used to predict the effective properties of a composite material by simulating the behaviour of the individual constituent materials and their interactions at the subscale. Traditionally, most computational homogenization schemes for analysis of composite systems [1][2][3] in general and viscoelastic composite systems [4,5] in particular, have been developed based on classical continuum mechanics, which is built upon the assumption of local action as well as smooth and continuous deformation. However, there are many mechanisms that give rise to processes in composite materials which invalidate these fundamental assumptions of the classical theory. ...
... In (17), 3 is a tensor-valued symmetric micromodulus function where c = 18k/πδ 4 is the bond force constant in the BBPD framework, and z 〈ξ〉 = Y 〈ξ〉 − Fξ. ...
This article presents a computational homogenization framework for viscoelastic composites within the framework of non-ordinary state-based peridynamic theory. The motivation to develop this framework stems from the desire to develop a homogenization scheme that can model processes and phenomena that are driven by nonlocal behaviour such as size effect and fracture for which frameworks based on the classical continuum theory lack the capability of modelling. The proposed framework was used to calculate the effective properties in both time and frequency domains of two viscoelastic matrix-inclusion composite systems, one with an elastic inclusion and viscoelastic matrix, and the other with viscoelastic inclusion and matrix. The results of calculations were found to compare well with results from the literature. A parametric study was also conducted to investigate the influence of nonlocal interaction on the effective properties by varying the horizon size. Results showed that increasing the degree of nonlocality reduces the stiffness of the composite system as well as increase its rate of creep. The capability to account for nonlocal interaction highlights the potential of this proposed scheme to provide a more comprehensive understanding of the behaviour of viscoelastic composite materials over a wide range of material behaviour.
... The material behaviour of the RVEs, which results into the constitutive law of the finite element can be derived either experimentally or can be obtained from separate micro-scale models. Micro-scale models are used frequently in multi-scale modelling approaches to simulate the behaviour of specific masonry patterns, which are used to express the behaviour of the full scale structure [181,182]. Although this approach effectively links the macro and micro scale behaviours, it is computationally costly and prone to errors due to certain simplification assumptions made in the micro-scale model (e.g. ...
... (e; eg. [5,182,74,9]) and (f; eg. [48], specifically for quasi-periodic bonds), both fulfill the scaleability, however, as (e) contains a full brick, rather than only cut pieces, it is favoured within this research. ...
... Within this section the continuum based d + /d − -damage model from Petracca et al. [183,182] shall be discussed with a focus on the applicability for the presented masonry. As the aim of this research is the simulation with thin walled shell-based formulations, the following relations are discussed in plane-stress state. ...
This thesis presents innovative methodological developments for a
seamless computer-aided design-integrated simulation and structural
assessment of masonry in a numerical multiphysics environment.
A numerically classified experimental program is processed to obtain a
quantitative classification of masonry, for which a novel computational
constitutive law is developed and presented. Furthermore, finite
element-based physics are enhanced to cope with the properties of
computer-aided design descriptions towards the demands of masonry
structures. With the presented avenues increased possibilities arise
in the structural assessment of buildings, including post-damage
load-carrying behaviors and limit stress states for various impact
scenarios. This is demonstrated in a selection of relevant benchmark
problems. With the presented choice of small-scale tests, an eventual
solution scheme towards the predictability by simulation of historic
and new buildings shall be introduced.
The development of the computer-aided design-integrated methods is
presented in a manner that reaches beyond the needs of masonry and
shall enlighten the general applicability of the proposed approaches.
The established technologies are introduced along with realized code
developments, specifically addressing a unified implementation for
a generic integration within various finite element software environments.
... The parameters needed for the definition of the material have been defined according to [34]: the peak (fcp), the elastic (fc0) and the residual (fcr) compressive strengths and the strain (εcp) at peak compressive strength. The compressive (Gc) and the tensile (Gt) fracture energies have been computed according to the equations proposed in [35]. In this case, the input fracture energies have been divided by the characteristic element length (lch) to obtain a response that is mesh-size independent. ...
