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The structural analysis of historic masonry churches subject to earthquakes is commonly based on two distinct approaches: that of the global response to seismic actions and that of the local analysis of a priori pre-determined collapse mechanisms. This is a conventional decoupling of the structural problem due to the difficulty of addressing the seismic vulnerability of individual parts from the modelling of the whole. The aim of this work is to establish a link between the global behavior of the church and the assessment of the local mechanisms, re-evaluating the value of modal analysis to be associated with non-linear seismic assessment. With this aim, a two steps procedure is proposed, where: the first step is based on the detection of the main vibration modes of the whole building with identification of the structural bi-dimensional macro-elements that are responsible for the overall seismic vulnerability, while the second step, is based on the non-linear finite element analysis of the previously identified macro-elements, to evaluate the failure pattern caused by the earthquakes. The procedure will applied to the case study of the Casamari Gothic church in Veroli (Italy).

This paper compares simple interatomic potentials for carbon nanostructures with hexagonal lattice, by investigating the in-plane and the out-of-plane tensile behaviour of single-layer graphene sheets. Attention is given both to potentials already considered in the literature and to a new one, which we call the damped DREIDING potential, in which damping functions are added to the DREIDING potential. For each potential, a calibration of its parameters and a focus on its performance are carried out in the in-plane context, by comparison with ab initio results of the rigidities and of the tensile limit properties, under periodic conditions. In addition, the damped DREIDING potential is used to perform in-plane tensile tests on both pristine and perforated single-layer graphene sheets of finite size. In the out-of-plane context, the calibration from ab initio results is only possible with reference to the rigidity. For the damped DREIDING potential, a sensitivity analysis, applied to a nanoindentation problem, on a pristine single-layer graphene sheet of finite size is provided. In doing so, a narrow range of value of the force needed to remove an atom from a sheet is given.

This work presents a numerical model to analyse the hygro-thermal behaviour of wooden bridge members. A multi-Fickian hygro-thermal model, previously implemented by some of the authors, is extended by including the dependency of wood sorption on temperature above and below zero degrees Celsius to predict moisture, temperature and relative humidity in wood under Northern European climates. The performance of the model in the presence of protective paints is particularly investigated. The finite element analysis based on the proposed model simulates the hygro-thermal behaviour of a glue-laminated beam of Älsvbacka Bridge located in Skellefteå (North of Sweden). The beam, coated by paints and claddings, was monitored by using wireless sensors in a previous research. Comparisons with the available measurements reveal that the numerical model is able to predict the moisture content in locations sheltered from rain and sun with moisture levels below the fibre saturation point. A study of the influence of different protective paints shows that the maximum and minimum moisture content at various depths along horizontal paths of the beam cross section, as well as the moisture gradients in different seasonal periods, are strongly affected by the type of paint. The proposed numerical approach is a promising tool to facilitate sensor-based monitoring techniques and to optimize the choice of protective paints for improved performance of timber bridges and other wooden structures under variable climates.

This paper deals with a numerical model for the buckling and post-buckling analysis of single-wall carbon nanotubes. Reasons of efficiency lead to the choice of a simple molecular statics model, wherein binary, ternary and quaternary atomic interactions are accounted for and described using Morse and cosine potential functions. The equations of the model are discussed in depth and the parameters of the potential functions are justified in the light of a comparison with ab-initio results. Several case studies regarding zigzag and armchair tubes of different aspect ratios, under compression, bending and torsion, are addressed with the aim of investigating the efficacy of the model and the role of the quaternary interactions, in contexts of both global and local behaviours.

This work provides a contribution to the critical dissection of interatomic potentials for carbon nanostructures (sp2 carbon nanoforms), within the framework of atomistic models. Within the vast family of empirical potentials, the discussion focuses on those characterized by only short-range interactions which, due to their simplicity, are suitable for a FEM implementation in Molecular Mechanics, and can be easily incorporated in continuum models, through appropriate constitutive identification procedures. After a first selection of the potentials on the basis of the stated criteria, their parameters are calibrated starting from the ab-initio results found in the literature. The performances of the potentials are compared in both armchair and zigzag tensile tests under periodic conditions and up to failure, and some considerations about their trend in terms of inner forces and couples are made. From this comparison the proposal of a new interatomic potential arises, which we call damped DREIDING and use to perform tensile tests on graphene sheets of finite size. The problem of the alleged auxeticity of graphene in the armchair direction is also discussed. This work provides a contribution to the critical dissection of interatomic potentials for carbon nanostructures (sp2 carbon nanoforms), within the framework of atomistic models. Within the vast family of empirical potentials, the discussion focuses on those characterized by only short-range interactions which, due to their simplicity, are suitable for a FEM implementation in Molecular Mechanics, and can be easily incorporated in continuum models, through appropriate constitutive identification procedures. After a first selection of the potentials on the basis of the stated criteria, their parameters are calibrated starting from the ab-initio results found in the literature. The performances of the potentials are compared in both armchair and zigzag tensile tests under periodic conditions and up to failure, and some considerations about their trend in terms of inner forces and couples are made. From this comparison the proposal of a new interatomic potential arises, which we call damped DREIDING and use to perform tensile tests on graphene sheets of finite size. The problem of the alleged auxeticity of graphene in the armchair direction is also discussed.

The paper deals with a numerical model for hexagonal boron nitride nanostructures. The model is developed in finite kinematics and takes into account binary, ternary and quaternary atomic interactions, described through the UFF potential with an ad-hoc set of parameters. Once validated with respect to ab-initio results of the tensile failure of boron nitride sheets under periodic conditions, the model is used to study the response of a sheet of finite size under traction, compression and shear.

The paper presents a study of defect-free achiral single-wall CNTs starting from a simple and effective molecular mechanics model (stick-and-spring), accounting for binary and ternary interactions at the atomic scale. The analytical expressions of the elastic constants related to the membrane behaviour of a Donnell thin shell are derived exploiting proper discrete homogenization tools and the results are compared with those of numerical analyses of the tubes under tensile, radial and torsional loads. By the analysis of the results, size and small scale effects are clearly highlighted and a discussion about their relevance is carried out.

The tensile behaviour and the pure shear behaviour of pristine and perforated single-layer graphene sheets are numerically investigated through a stick-and-spring model including both material and geometric non-linearities. The model is formulated in finite kinematics and the atomic interactions are modelled through the modified Morse potential, tuned with an improved set of parameters. The progression of the failure process of the sheets is numerically reconstructed using the arc-length strategy. The failure profiles are displayed and discussed. A continualization of the obtained results is made. The engineering strains and stresses and the second Piola and Green–Lagrange tensors are computed and compared with results given in the literature.

The paper presents a nonlinear buckling analysis of single-layer graphene sheets using a molecular mechanics model which accounts for binary, ternary and quaternary interactions between the atoms. They are described using a geometrically exact setting and by the introduction of Morse and cosine potential functions, equipped with an appropriate set of parameters. We examine the critical and post-critical behaviours of graphene, under compression in the zigzag and in the armchair directions, and shear. Our findings show the suitability of standard thin-plates theory for the prediction of simple critical behaviours under various edge constraint conditions.

The paper presents a numerical study of defect-free single-wall carbon, boron nitride and silicon carbide armchair and zigzag nanotubes, through a simple stick-and-spring model, based on Morse and cosine potential functions. The study investigates the relaxed configuration of the tubes and gives a comprehensive evaluation of their elastic constants, which is performed by framing tensile, torsional and radial tests within the membrane behaviour of a Donnell thin shell model. Extensive comparisons with reference ab-initio results are given and used to refine some parameters of the potential functions for hexagonal silicon carbide nanomaterials.

The force constants related to the bond stretching and angular variation of boron nitride, silicon carbide, aluminium nitride and gallium nitride nanosheets are directly evaluated from ab-initio reference solutions of the Young’s modulus and the Poisson’s ratio. To this end, the analytical expressions of the elastic constants of a generic monolayer hexagonal diatomic sheet are derived, starting from its sticks-and-springs molecular mechanics model, through proper tools of the homogenization of periodic discrete media. Numerical benchmark assessments are given.

A geometrically nonlinear beam model suitable for describing complex 3D effects due to non-uniform warpings including non-standard in-plane distortions of the cross-section is presented and applied to the buckling analysis of beams. Each section is endowed with a corotational frame where statics and kinematics are described using a refined linear elastic model which exploits a semi-analytical solution of the Cauchy continuum problem based on a FEM discretization of the cross-section. The stress field in this way is fully 3D, allowing both the exact recovery of the standard Saint Venant solution and the consideration of some additional relevant strain modes of the cross-section that are evaluated in a simple and effective way. Numerical results are presented and compared with 3D shell reference solutions obtained by using the commercial code ABAQUS.

Several nanomechanics formulations based on common two and three-body bonding potentials are compared. Numerical simulations and analytical approaches are used to investigate the not negligible differences among the predictions of the in-plane elastic constants of graphene sheets in the literature, separately exploring the role of the potentials and that of the structural descriptions (beams and trusses) of the original molecular mechanics (MM) model. The energetic differences between the structural models and the MM model are highlighted through exact discrete homogenization procedures. In so doing, some theoretical expressions of the graphene elastic constants available in the literature are recovered and supported by the numerical experimentation. The results provide also an assessment of the accuracy of some potentials largely employed in the literature with respect to several ab-initio reference solutions and the experimental measurements available. Some suggestions towards a reparametrization of the modified Morse potential are consequently formulated.

A model for beams with heterogeneous and anisotropic cross-section is presented. A semi-analytical approach which exploits a FEM discretization of the cross-section is used to derive a Ritz–Galerkin approximation of the stress and displacement fields. In this way the Saint-Venant solution is easily generalized to generic composite sections and additional variable warping effects are also included in the model. Numerical results relative to composite beams with compact or thin walled section are presented and compared with full 3D analyses.

A linear model for beams with compact or thin-walled sections and heterogeneous anisotropic materials is presented. It is obtained by means of a Ritz–Galerkin approximation using independent descriptions of the stress and displacement fields. These are evaluated by a preliminary semi-analytic solution based on a finite element description of the cross section. A coherent definition of the deformations and stresses is obtained which includes both the generalized Saint Venant solution for generic materials and some significant additional effects, due to out-of-plane warping and section distortions. The so-built 1-D model maintains the richness of the 3-D solution using a small number of variables.

The monitoring of timber structures exposed to natural climate fluctuations during their service life is an important topic for both their serviceability and safety. Numerical methods based on the recent advances in hygro-thermal modelling of wood can integrate the usual sensor-based monitoring techniques by reducing the maintenance costs for timber structures. In this paper, a 3D full coupled analysis based on the multi-Fickian theory with sorption hysteresis of wood is implemented in Abaqus FEM code by defining a new finite element in a user subroutine. To verify the method, the hygro-thermal behaviour of a glulam beam tested in laboratory under variable humidity within a previous research is analysed and the numerical values of moisture content are found to be in agreement with the experimental data. Furthermore, a numerical case-study of a glulam cross section under real climate variations is presented and the related results show the capability of the method to predict the moisture states in each points of the glulam member under continuously variable humidity and temperature.

A new linear model for beams with compact or thin-walled section is presented. The formulation is based on the Hellinger-Reissner principle with independent descriptions of the stress and displacement fields. The kinematics is constituted by a rigid section motion and non uniform out-of-plane warpings related to shear and torsion. The stress field is built on the basis of the Saint-Venant (SV) solution and with a new part to describe the variable warping. The formulation of a finite element with exact shape functions made possible to validate the beam model avoiding discretization errors.

The monitoring of timber bridges during their service life is important for the maintenance plans of these structures. Numerical modelling can integrate the monitoring techniques by reducing the needed inspections and the maintenance costs. In this paper a 3D computational model based on a well assessed multi-Fickian theory is implemented in Abaqus FEM code. The hygro-thermal response of a timber pedestrian bridge is simulated during a period of its service life. The numerical results are in agreement with measurements taken by a sensor-based technique. Conclusions are given on the moisture gradients which could generate the so-called moisture induced stresses (MIS).

A new geometrically nonlinear model for homogeneous and isotropic beams with generic section including non-uniform warping due to torsion and shear is derived. Each section is endowed with a corotational frame where statics and kinematics are described using a 3D linear elastic model which extends the Saint-Venant solution to non-uniform warping cases. The algebra of change of observer and a mixed variational principle give the model in terms of generalized parameters. Using a mixed interpolation the model is implemented within a FEM Koiter analysis highly sensitive to the geometrical coherence of the formulation.

Surface densification of solid wood increases the density on the surface, when compressed by single side heated press. A recent experimental study has pointed out the influence of the process parameters on the development of the density profiles in the modified samples. Numerical modelling can help to optimize the experimental work which is often time consuming and laborious due to the large amount of experiments required to check the influence of the pressing parameters. In the present work, a FEM simulation of the hygro-thermal behaviour of wood under surface densification is proposed by using a three-dimensional hygro-thermal model based on earlier literature approaches. The model is implemented in a user subroutine of the FEM code Abaqus starting from the definition of a weak form of the governing hygro-thermal equations of the problem. The numerical profiles of moisture content and temperature during the wood densification process are simulated for some wood specimens tested in a previous study. Conclusions are given on the relationship between these profiles and the experimental density profiles due to different process parameters.