Although masonry represents one of most ancient construction material, the numerical simulation of the actual behavior of masonry structures is still a very complex issue. The main concern is related to the difficulty to characterize a reliable simulation of the high non-linear degrading cyclic response of masonry material whose great variability of mechanical characteristics makes difficult to define a general constitutive law to be applied for all masonry structures (Lourenço et al., 1998; Asteris et al., 2014). The non-linear dynamic behavior of a masonry structures, subjected to earthquake loadings, is also characterized by a complex interaction between in-plane and out-of plane response of masonry walls and is often further complicated by the presence of structural elements with curved geometry such as arches, domes, and vaults. Masonry material provides its mechanical contribution also in mixed-masonry structures, like confined masonry and infilled masonry buildings; in these latter cases, the numerical simulations require the modeling of the complex non-linear interaction of the different structural members contributing to the global bearing capacity of the structural system (Asteris et al., 2011; Caliò and Pantò, 2014).

In the scientific literature, there are many significant examples of applications of the non-linear finite element method (FEM) to historical masonry buildings and churches (Mele et al., 2003; Betti and Vignoli, 2008, 2011; Araujo et al., 2012; Lourenço et al., 2012; Barbieri et al., 2013; Milani and Valente, 2015), however refined FE approaches (Lofti and Shing, 1994; Anthoine, 1997; Gambarotta and Lagomarsino, 1997; Lourenço and Rots, 1997; Berto et al., 2002; Macorini and Izzuddin, 2011) coupled with sophisticated constitutive laws, require a huge computational cost and advanced abilities in the model implementation and in the interpretations of the results. On the other hand, structural engineers need simple and efficient numerical tools, whose complexity and computational demand should be appropriate for practical engineering purposes. For these reasons, in the last decades, many authors proposed simplified or alternative methodologies to predict the non-linear seismic behavior of unreinforced masonry (URM) structures, particularly oriented to buildings (D’Asdia and Viskovic, 1995; Braga et al., 1998; Brenchich et al., 1998; Magenes and La Fontana, 1998; Kappos et al., 2002; Caliò et al., 2005; Chen et al., 2008; Marques and Lourenço, 2011; Raka et al., 2015). Marques and Lourenço (2011) report a comparison between different simplified approaches currently used in academic research and engineering practice. However, most of the simplified methods, currently used in practical engineering, restricted to in-plane behavior of masonry walls, are unsuitable for those masonry structures dominated by the out-of plane seismic response, as in the case of historical monumental buildings and churches. An alternative approach to the non-linear FEM is represented by the rigid-body spring models, specifically formulated with the aim of approximating the macroscopic behavior of masonry walls with reduced degrees of freedom. Some valuable applications of this approach are relative to historical masonry buildings (Casolo and Peña, 2007; Casolo and Sanjust, 2009). A comprehensive review of the current development on numerical issues on masonry mechanics is reported in Lourenço (2002). In the latter works, it is also highlighted that a complex analysis tool does not necessarily provide better results than a simplified one.

In this paper, an innovative modeling strategy for the simulation of the non-linear behavior of URM structures, under static and seismic loadings, capable of accounting for the in-plane and out-of plane behavior of masonry as well as curved geometry masonry structures, is presented. The approach here proposed is based on the concept of macroelement discretization (Caliò et al., 2012a) and has been conceived with the aim of capturing the non-linear behavior of an entire structure through an assemblage of discrete macroelements characterized by different levels of complexity according to the role played in the global model. The basic element has been initially (Caliò et al., 2005) developed for the simulation of the in-plane response of masonry walls and has already received several numerical and experimental validations (Lourenço, 2002; Marques and Lourenço, 2011; Caliò et al., 2012a; Pantò et al., 2015). The basic in-plane element is currently used by the engineering community for masonry building modeling by means of the 3DMacro computer code implementation (Caliò et al., 2012b), endowed with simplified input and output graphical user interfaces. This plane element can be represented through the aid of a simple and unambiguous mechanical scheme since it can be regarded as an articulated quadrilateral with four rigid edges and four hinged vertices connected by two diagonal non-linear springs. Each of the rigid edges can be connected to other elements by means of a non-linear zero-thickness interface. This novel approach has been also recently successfully applied and validated for mixed reinforced concrete–masonry structures and for confined masonry buildings (Caliò et al., 2008; Caddemi et al., 2013; Caliò and Pantò, 2014; Marques and Lourenço, 2014). In this latter case, the infills are modeled by 2D “geometrically consistent” macroelements, while the reinforced concrete frames are modeled by concentrated-plasticity beam columns. The adopted term “geometrically consistent” is used to emphasize that the geometry of the macroelement is consistent with the actual two-dimensional geometry of the infill. Also, in the presence of openings the geometrical consistence is assured through a mesh of macroelements.

However, the basic plane element has been conceived only for the simulation of the non-linear response of masonry walls in their own plane, since the out-of plane response is ignored. To overcome this significant restriction, common to several macroelement simplified approaches in the literature, the plane macroelement has been modified by introducing a third dimension and the relevant additional degrees of freedom (Pantò et al., 2017a; Pantò, 2007; Caddemi et al., 2014). The kinematics of the enriched 3D-macroelement is governed by seven Lagrangian parameters only and allows an efficient simulation of the in-plane and the out-of plane response of masonry walls.

One of the advantages of the proposed macroelement strategy consists in a reduced computational cost if compared to the traditional non-linear finite element modeling. However, another benefit relies on the adopted mechanical calibration strategy that, being based on straightforward fiber discretization, allows the use of simple uni-axial constitutive laws and leads to a very easy interpretation of the numerical results. Based on the above issues, the macroelement approach can be considered not only a reliable numerical tool for academic researches but also an efficient practice-oriented platform.

Many monumental masonry constructions are characterized by the presence of structural elements with curved geometry, such as arches, vaults, domes whose role cannot be neglected in a reliable numerical analysis. For this reason, a further enrichment of the proposed three-dimensional macroelement towards a more general macro-shell-element, able to discretize curved geometry monumental structures, has been introduced (Calió et al., 2010; Cannizzaro, 2010; Caddemi et al., 2015). The shell macroelement was conceived as the extension of the spatial element. Its nucleus is now constituted by an irregular articulated quadrilateral still characterized by four rigid layer edges whose orientation and size are related to the shape of the element and to the thickness of the modeled masonry portion. This more general macroelement strategy is mainly devoted to the numerical simulation of the seismic behavior of historical masonry structures (HMS), and it has been implemented in the software code HiStrA (Historical Structures Analysis) (Caliò et al., 2015), which simplifies the modeling of historical structures by means of several wizard generation tools, suitable to manage complex curved geometries.

The aim of this paper is to provide a comprehensive review of the proposed discrete macroelement strategy and to show its capabilities through different applications to significant benchmark structures for which experimental and/or numerical results are reported in the literature. The paper, although containing a review of different macroelements already proposed by the authors, highlights the novelties of the proposed approach with respect to the existing simplified methods for masonry and monumental structures. Another target of this work is to illustrate a comprehensive parsimonious modeling strategy from the simplest cases, i.e., the regular plane element, to more complicated structural scenarios, e.g., infilled frame structures (IFS) or historical masonry constructions. This paper, although recalling several results already presented in the literature, clearly highlights the proposed strategy which is based on the use of different discrete macroelements characterized by a different level of complexity according to the role played in the overall structural idealizations. All the elements can interact in the same environment leading to a powerful numerical strategy whose computational demand is extremely low if compared to those related to classical non-linear FEM simulations or to rigid-spring-element approaches. The low computational cost and the easiness in the interpretation of the results make this method particularly suitable for the engineering community as well as for the research on the seismic assessment of cultural heritage buildings.

The macroelement strategy, proposed by the authors in the last years for the non-linear analysis of masonry structures, has been defined according to an original approach within the framework of a discrete element formulation strategy. Such an approach is based on the subdivision of the structure under consideration in several macro-portions (wall, arch, vaults, and so on); then, after a homogenization of the mechanical properties of the components (mortar and units), each portion is regarded as an equivalent continuum whose mechanical properties can be assumed as isotropic or orthotropic depending on the masonry texture. The next step is the discretization of each macro-portion by means of a mesh of an appropriate original macroelement (2D, 3D, or shell). In Figure 1, it is qualitatively reported the subdivision of a part of a masonry dome by means of several macro-portions that, according to a macroelement strategy, will be represented by the corresponding macroelements.

In this approach each macroelement, that is not rigid, interacts with the adjacent elements through non-linear zero-thickness interfaces and the non-linear behavior of the investigated structure is then captured through an assemblage of macroelements, characterized by different level of complexity according to the role played in the global model.

According to the proposed modeling strategy, the assemblage of the global stiffness and mass matrixes is not based on assigning degrees of freedom to each node and on a subsequent condensation of some of them because of the internal constraints due to the rigid edges of the quadrilateral. On the contrary, the degrees of freedom are directly assigned to the elements and are exactly those strictly necessary. In particular, each quadrangular element is endowed by four [for the plane element (Caliò et al., 2012a), Figure 2A] or seven [for the spatial models (Pantò et al., 2017a; Calió et al., 2010), Figures 2B,C] independent degrees of freedom; then, each discrete interface inherits the degrees of freedom from the two quadrangular elements which are connected by it through a compatibility matrix to be built. The coupling of the degrees of freedom of the generic element with the other is hence ruled by the presence of the connecting interfaces.

In Figure 2, the mechanical scheme of the macroelement adopted for masonry structure modeling is qualitatively shown together with its evolution. The macroelement is based on a quadrilateral of rigid beams connected by four hinges. One diagonal spring rules the shear diagonal behavior and zero-thickness interfaces, along the four edges, govern the interaction with the adjacent elements. In particular, the element showed in Figure 2A, that is the first basic element proposed in Caliò et al. (2005, 2012a), possesses only the in-plane degrees of freedom and has been conceived for the simulation of the non-linear response of regular plane walls. Its detailed description and main insights are reported in the Section “The Plane Macroelement” for URM buildings and in the Section “The infilled frame structures” for IFS. In Figure 2B, the equivalent scheme of the first proposed three-dimensional element (Pantò et al., 2017a; Pantò, 2007; Caddemi et al., 2014), which implies the addition of the out-of-plane degrees of freedom, is reported. This macroelement is able to account for both the in-plane and out-of-plane behavior of masonry walls, a description of the element with some numerical validations are reported in the Section “The Spatial Three-Dimensional Element.” Finally, in Figure 2C, a further upgrade proposed in Calió et al. (2010), Cannizzaro (2010), and Caddemi et al. (2015) includes the removal of the hypothesis of constant thickness for the element and the adoption of skew interfaces able to properly “follow” a curved geometry layout, thus allowing the modeling of masonry vaults and domes. A brief review of this three-dimensional shell-element and some numerical validations are reported in the Sections “The Shell Element for Modeling Curved Geometry Structures” and “Numerical Examples of Full Scale Structures.”

The basic element can be described by referring to a simple mechanical representation in which the element is regarded as a plane articulated quadrilateral endowed with along-sides non-linear zero-thickness interfaces (Caliò et al., 2005, 2012a). The mechanical behavior of the element is governed by along-edge non-linear interfaces plus the in-plane deformability of the quadrilateral whose behavior is related to a single degree of freedom only, Figure 2A. To adopt a simple fiber discretization, the zero-thickness interfaces have been conveniently represented in Figure 2A as a regular distribution of non-linear links orthogonal to the interfaces. The shear-sliding behavior along the interfaces, associated with the relative motion in the direction of the interface, can be efficiently described through a single longitudinal spring. The kinematics of the mechanical scheme after a proper calibration procedure of the non-linear links is capable of simulating the main in-plane collapse failure modes of a masonry panel: flexural failure, diagonal shear failure and sliding shear failure. In spite of its simplicity, the assemblage of these elements allows the simulation of the global non-linear response of masonry buildings; however, in this model, the out-of-plane response of the masonry walls is not taken into account.

Each discrete element exhibits three degrees of freedom associated with the in-plane rigid body motion, plus an additional degree of freedom, needed for the description of the in-plane shear deformability. The deformations of the interfaces are associated with the relative motion between corresponding panels; therefore, no further Lagrangian parameter has to be introduced to describe their kinematics. The adopted model has the advantage of interacting with the adjacent elements along the whole perimeter, thus allowing the possibility of using different mesh discretizations as highlighted in the following paragraphs.

To make the simulation of the non-linear behavior of a masonry structure effective, it is necessary to infer the mechanical parameters of the model by means of an equivalence between the masonry material and the reference macro-model characterized by simple but reliable constitutive laws. This equivalence is enforced according to a straightforward fiber calibration procedure, uniquely based on the main mechanical parameters of the masonry (Caliò et al., 2005). It is worth to notice that each macroelement inherits the plane geometrical properties of the corresponding modeled masonry portion. As a consequence, differently from the simplified models based on the equivalent frame element, the model is geometrically consistent to the corresponding modeled masonry wall.

In the following subsection, some significant examples of simple structures are considered to provide a validation of the model. In particular, single masonry panel models, characterized by different geometries and subjected to vertical loads and increasing monotonic horizontal forces, are considered.

The macroelement can also be efficaciously adopted for Infilled Frame Structures (IFS) modeling. In the latter case, a hybrid approach is applied: the surrounding frame is modeled using lumped plasticity beam–column elements while the non-linear response of the infill is modeled by means of the plane macroelement, already described in the previous section. The frame element interacts with the masonry panels by means of non-linear-links distribution along discrete interfaces. Each interface is constituted by n transversal non-linear links and a single longitudinal non-linear link. The flexural interaction between the panel and an adjacent beam is governed by the four degrees of freedom of the beam associated with its two ends and by the n internal degrees of freedom associated with the springs of the interface. For a more accurate evaluation of the non-linear behavior of the frame element, it has been assumed that plastic hinges can occur in each sub-beam element between two non-linear transversal links. This latter assumption provides a reliable frame element model since it is able to embed the occurrence of plastic hinges at different positions and it is consistent with the adopted level of discretization for the infill interface.

The effectiveness of the masonry infill model relies on a suitable choice of the mechanical parameters of the macroelement inferred by an equivalence between the masonry media and a reference continuous model characterized by simple but reliable constitutive laws. This equivalence, as already explained in Section “The Mechanical Characterization,” is based on a straightforward calibration procedure that exploits the main mechanical parameters of the masonry only, according to an orthotropic homogeneous medium, as detailed in Caliò and Pantò (2014). In Figure 5, a typical discretization of a full infill frame (Figure 5A) and an infill frame characterized by a single central opening (Figure 5D) are shown. Figures 5B,E report the corresponding discretization according to a basic mesh of the infill, whereas the representations of Figures 5C,F are relative to a more refined mesh of the infill. This aspect is particularly important in the modeling of infilled frames since it allows a better description of the interaction masonry frame, also in the presence of window or door openings. It is important to notice that the macro-model has the great advantage, compared to the equivalent strut element approaches (Polyakov, 1960), to inherit the plane geometrical properties of the corresponding modeled masonry portion avoiding the introduction of an effective dimension of the element. Despite its mechanical simplicity, the model is able to simulate the main collapse mechanisms that can be involved in infilled frames.

It is worth noticing that the proposed approach is also able to identify combined mechanisms and the simultaneous presence of damage corresponding to different failure modes. To explain this aspect, Figure 6 shows a qualitative representation of the main in-plane failure collapse mechanisms and their simulation by the equivalent macro-model, namely the Corner Crushing mode (Figure 6A), the Diagonal Cracking mode (Figure 6B), the Sliding Shear mode (Figure 6C), and the Frame Failure mode (Figure 6D) (Caliò and Pantò, 2014). The main failure mechanisms typical of IFS are identified comparing them with the corresponding schemes associated with the proposed model, as they were independent collapse mechanisms. In practical experience, it is frequent to have combined mechanisms; however, in this case, they are shown separately to demonstrate the capability of the proposed model of grasping them. For the latter reason, the detachment of the frame from the masonry is shown only in Figure 6A and not in the others (Figures 6B–D). Such mechanisms are reported adopting the convention that the links in compression are reported in blue while the links in tension are reported in red; in addition, plastic hinges occurring at the contouring frame are reported in red.

A non-trivial spatial extension of the plane macroelement introduced in Section “The Plane Macroelement,” was the extension to a three-dimensional macroelement hereafter described. The element upgrade requires three additional degrees of freedom for the description of the out-of-plane kinematics as well as the introduction of further non-linear links to account for the three-dimensional mechanical behavior of the element. The kinematics of the spatial macroelement is therefore governed by seven degrees of freedom, able to describe the rigid body motions and the element in-plane shear deformability. The interaction of the spatial macroelement with the adjacent elements, or the external supports, is still ruled by zero-thickness interfaces. Each interface is composed, according to a fiber discretization, by m rows of n transversal non-linear springs (N-links), as showed in Figure 8A. The in-plane sliding motion between two continuous panels is governed by a single longitudinal in-plane spring and two additional springs oriented orthogonally to the plane of the element (Figure 8B). The latter two additional springs govern both the out-of-plane sliding mechanisms and the torsion around the axis perpendicular to the plane of the interface. The zero-thickness interface between adjacent elements governs the membrane, bending, sliding, and torsional behaviors, while the in-plane pure shear deformability of the element is controlled by the internal diagonal spring as in the in-plane basic macroelement. The transversal N-links of the interface encompass the axial and the three-dimensional flexural behavior of the panel, assuming for the masonry an equivalent orthotropic homogeneous material. Each transversal N-link represents the non-linear behavior of the corresponding fiber, along a given material direction, see Figure 8A. Those links are calibrated assuming that the masonry strip is a homogeneous inelastic material with a post elastic linear softening behavior governed by two different values of fracture energy, for tension and compression, following the procedure briefly described in Section “The Mechanical Characterization” and reported in detail in Cannizzaro and Lourenço (2017). The calibration procedures for both diagonal and in-plane sliding spring follow the same strategy already adopted for the plane macroelement (Caliò et al., 2012a).

The two longitudinal out-of-plane links of the interfaces are calibrated to reproduce the elastic out-of-plane shear deformation of the influence masonry volumes associated with the link, according to the shear modulus G of the masonry (Figure 8B). Once the elastic shear out-of-plane stiffness has been calibrated, the relative distance d between the two springs (Figure 8B) is set according to a criterion which guarantees the retrieval of the elastic torsion stiffness associated with the reference continuous volumes, as better highlighted in Table 2. More details on this calibration procedure can be found in Pantò et al. (2017a).

The model presented in the Section “The Spatial Three-Dimensional Element” (Pantò et al., 2017a) allows the simulation of the contemporary action of in-plane and out-of-plane forces on masonry walls based on a regular geometry. According to this model, each element belongs to a structural plane, its shape is rectangular, and characterized by a constant thickness. To overcome these geometrical limits and to allow modeling more complex geometrical layouts, a further extension of the model was proposed in Cannizzaro (2010) and Caddemi et al. (2015). This extension was motivated by the need of applying the macroelement approach to historical and monumental masonry structures, and in particular to two main structural typologies as follows:

plane structural elements with an irregular geometry, such as, walls with irregular elements or arches, for which a mesh of rectangular element cannot be adopted;

The study of such structural typologies is further complicated by the complex geometry, which connotes them. The corresponding upgrades of the macroelement were needed since the static and dynamic equilibrium of curved masonry structures is mainly guaranteed by their shapes. The most significant novelties of the improved element can be summarized in the following features:

interfaces are no longer orthogonal to the plane of the element, thus allowing to follow the curved geometry of the structure;

A qualitative representation of this upgraded element is reported in Figure 2C. In spite of the complications due to the curved geometry, the model still keeps the original computational effort since its kinematics is ruled by seven degrees of freedom (six rigid body motion degrees of freedom and one associated with the in-plane shear deformability). The upgrades of the element, shortly described in the following, imply substantial modifications of the calibration procedure to account for the more complex geometry of the element.

Regarding the transversal springs (N-links) of the inter-element interfaces, which are still calibrated according to a fiber approach, the upgraded geometry implies that each link corresponds to a prismatic fiber, whose cross-sectional area varies with a parabolic trend. The grid of the fibers’ projections on each interface is no more regular to account for the geometric distortion according to an isoparametric correspondence between spatial coordinates and intrinsic regular coordinate system. The non-linear sliding links are three in each interface, just like for the regular spatial model: one link along the axis of the interface (in-plane sliding link) and two orthogonal to the axis and still lying on the plane of the interface (out-of-plane sliding links). The calibration strategy follows the same philosophy of the previous spatial regular model. Since those links have to simulate the occurrence of sliding along the bed joints, their non-linear behavior is closely affected by friction phenomena; for this reason the yielding domain accounts for the influence of the normal force acting on the interface. This calibration approach strictly follows the procedure employed for the regular spatial element; however, it accounts for the more complex geometry of the curved element in terms of irregular shape of the interface. In the subdivision of an arbitrary shell into flat elements, both triangular (Triang) and quadrilateral (Quad) elements should generally be used (Figure 10). The triangular elements are assumed to be rigid in their own plane and are therefore characterized by six degrees of freedom only.

A detailed description of the mechanical characterization of this non-trivial shell discrete element is outside the purpose of the present paper that is oriented to a methodological description of this computationally effective approach aiming at demonstrating its suitability for practical applications devoted to the seismic assessment of existing masonry structures; in particular, the discrete macroelement here described is mainly devoted to the numerical simulation of the non-linear response of historical and monumental structures. More details on the calibration procedures can be found in Cannizzaro (2010).

Numerical and experimental validations of the proposed approach with reference to full scale structures can be found in Pantò et al. (2016, 2017b). Here some results reported in Pantò et al. (2017b) are recalled with the aim of showing a detailed and critical numerical comparison between the proposed discrete modeling approach and a refined finite element approach on a single-nave church, severely damaged by the Italian 2012 earthquake, which was analyzed by using both procedures. This numerical validation was performed both in the linear and non-linear fields through linear modal analysis and non-linear pushover analyses. The example under consideration is the St. Venerio church located in Reggiolo (Emilia Romagna region, Italy), 20 km far from the epicenter of the earthquake that struck the Emilia Romagna Italian region on 2012 May 29th. All the geometrical and mechanical details of the church can be found in Pantò et al. (2017b). The church is entirely built with clay bricks and lime mortar, often used in the nearby area for similar historic chapels.

The 2012 Emilia earthquake caused severe damages to the church: the timber roof and the main vault partially collapsed, a partial overturning mechanism of the main façade and the apse occurred and out-of-plane and in-plane damages were observed in the façades (Giresini et al., 2014).

The non-linear finite element model of the entire church was implemented in ABAQUS CAE 6.12 according to the Concrete Damaged Plasticity material (Abaqus 2014) (Giresini et al., 2014). The discrete macroelement model was developed by using the software HiStrA (Caliò et al., 2015).

The mesh discretization of the discrete model has been chosen to obtain a parsimonious model of the entire church, characterized by a reduced number of computational elements and degrees of freedom, compared to the finite element model. The FEM model possesses 114,936 degrees of freedom whereas the HiStrA model is characterized by 15,060 degrees of freedom.

In this paper, a numerical strategy aiming at simulating the non-linear behavior of masonry structures is presented. The proposed numerical model, which belongs to the framework of the simplified models, is based on a simple mechanical scheme that consists of a hinged quadrilateral, endowed with a diagonal link to govern the in-plane diagonal shear behavior, and contouring interfaces that rule the interaction with contiguous elements.

The proposed approach appears to be a fair compromise between oversimplified models (limit analysis or equivalent frame models) and accurate models based on cumbersome strategies, which require an expert interpretation of the results. The basic model, originally conceived for the simulation of masonry walls loaded in their own plane was repeatedly upgraded, progressively increasing the structural typologies that the proposed strategy is able to model. In particular, within the scope of the numerical simulation of ordinary buildings with box behavior (the out-of-plane behavior is considered inhibited), interaction with frames contouring a masonry panel was enabled, thus allowing the numerical simulation of both unreinforced masonry structures (URM) and infilled masonry structures (IFS).

Aiming at the numerical modeling of historical masonry structures (HMS), two further upgrades were considered. First, the out-of-plane degrees of freedom were enabled to assess the out-of-plane behavior of masonry walls; then, a further improvement allowed simulating masonry structures with a curved geometry. Finally, by ruling the interaction between structural elements in correspondence of their intersections, full non-linear simulations of large historical masonry constructions were performed. The progressive improvements were obtained simply extending the calibration procedure of the links according to the different peculiarities of the model at the various stages of complexity. However, the philosophy of the model was kept the same for all the considered advances of the model, that is, the calibration is always straightforward and based on the same concepts.

Several validations of the model were presented consistently with each of the described stage. The results show that the proposed strategy appears to be reliable in all the considered cases and that it represents an original approach to the non-linear assessment of ordinary masonry buildings, historical and monumental structures.

IC: substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; drafting the work or revising it critically for important intellectual content; final approval of the version to be published; and agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. SC: substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; revising critically the work for important intellectual content; and agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. BP and FC: substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; and drafting the work or revising it critically for important intellectual content.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.