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Over the last two decades, interest in the applications of graphene and carbon nanotubes has continuously grown in a variety of fields, including microelectronics, sensoring and actuation systems, energy generation and storage, biotechnologies and composite materials. In parallel, many researchers have also investigated nanomaterials consisting of elements other than carbon (C), including boron (B), nitrogen (N) and silicon (Si). Some examples are boron nitride (BN) and silicon carbide (SiC) nanosheets and the relative nanotubes. Similarly to their C analogues, these nanomaterials exhibit exceptional thermal and mechanical properties (e.g., low density, high thermal conductivity, high tensile stiffness and strength). Moreover, the different atomic composition leads to some specific properties, such as stronger resistance to oxidation and chemical stability at high temperatures, giving them advantages over C nanomaterials in harsh environments. As of now, these nanomaterials have drawn attention in different technological fields, including the composites, the manufacture of semiconductors and hydrogen storage. In addition, BN compounds can also be cleaned and reused by means of heating and burning in air, are biocompatible, have low friction coefficient, have excellent sorption performance and are hydrorepellent. For these reasons, they are studied also for applications in medicine (e.g. drug delivery), as lubricants and for water purification from oil, solvents and dyes. The effective exploitation of these nanomaterials goes hand in hand with in-depth knowledge of their physical behavior. Electronic, optical and mechanics properties are crucial and, moreover, also mutually interacting, even with the possibility of tuning the former trough control of deformation [7]. Knowledge of the mechanical behavior of these nanostructures is also related to the availability of predictive models, e.g., provided by ab-initio methods, by molecular dynamics (or statics) mechanics, but also by continuum mechanics and structural mechanics. In the context of linearized models, aimed at determining just elastic moduli, the cost of computationally onerous methods is not prohibitive; on the contrary, when the mechanical behaviour is highly non-linear, e.g., in post-buckling behaviour, in case of mode interaction or in fracture problems, the recourse to models as simple as possible becomes preferable. In the present paper a molecular mechanics model diatomic nanomaterial with hexagonal nanostructure is presented. The model is equipped by simple potentials, incorporating binary, ternary and quaternary atomic interactions. The parameters for BN sheets and tubes are derived. Numerical examples regarding linear and nonlinear behaviours of BN sheets and tubes are presented.

From about twenty years carbon-based nanostructures are a real challenge for the scientific community, for their enormous technological potential in several contexts of application, including microelectronics (e.g., conductive inks and flexible films), sensoring and actuating systems (e.g., gas sensors), energy generation and storage (e.g., photovoltaic cells, hydrogen storage, supercapacitors), biotechnologies (e.g., membranes for water filtration, gas separation, DNA sequencing) and composites. Their effective exploitation goes hand in hand with in-depth knowledge of their physical behavior. Electronic, optical and mechanics properties are crucial and, moreover, also mutually interacting, even with the possibility of tuning the former trough control of deformation. Knowledge of the mechanical behavior of these nanostructures is also related to the availability of predictive models, e.g., provided by ab-initio methods, by molecular dynamics (or statics) mechanics, but also by continuum mechanics and structural mechanics. In the context of linearized models, aimed at determining just elastic moduli, the cost of computationally onerous methods is not prohibitive; on the contrary, when the mechanical behaviour is highly non-linear, e.g., in post-buckling behaviour, in case of mode interaction or in fracture problems, the recourse to models as simple as possible is necessary. In the present paper a molecular mechanics model, equipped by simple potentials, incorporating binary, ternary and quaternary atomic interactions, is presented and the choice of the parameters of the given potentials is explained. The model is implemented in a numerical algorithm of step-by-step analysis with the objective to provide the equilibrium paths also in advanced post-buckling. Both the accuracy of the model and the reliability of the implementation are valued by means of a tight comparison with results in the literature of Solids State Physics.

In the last years carbon nanotubes (CNTs) have received considerable attention, due to the wide number of applications in electronic nanodevices, energy generation and storage, biotechnologies, composites. The study of the CNTs mechanical behaviour plays an important role for their manufacturing and integration in devices, for tuning their performances in certain applications as well as for controlling the mechanics of their composites. For this reason, considerable research efforts have been done for modelling the CNTs mechanical behaviour through the solid state physics methods, molecular mechanics models or continua. The most of the existing literature has focused only on the CNTs linear behaviour, while there is a lack of studies in the nonlinear range, especially of buckling. With this in mind, a nonlinear molecular mechanics model of single-wall CNTs is presented. The model accounts for standard binary and ternary interactions between the atoms and for dihedral angles. Numerical analyses regarding the buckling of single-wall CNTs are addressed directly at the nanoscale. The equilibrium paths and the deformed configurations are critically discussed in comparisons with 1D models endowed with suitable microstructure and considerations on the role of the various energy contributions are also provided.

Single-layer graphene sheets (SLGSs) are the basic structural element of several carbon allotropes, including graphite, fullerenes and carbon nano-tubes (CNTs). Due to their remarkable mechanical properties, extensive interests have been recently devoted to characterize their behaviour at nanoscale in order to investigate also the performance of advanced composites based on their inclusions. However, the evaluation of SLGSs mechanical properties in a direct experimental way is considered a difficult task because of the technical difficulties and the costs involved in the manipulation of nanoscale objects. For these reasons several modelling tools have been proposed varying from continuum models to atomistic approaches that account for the discrete nature of the matter. The most of the existing literature has focused only the evaluation of the elastic constants and of the force constants of the interatomic potentials, instead much less studies have been made about the nonlinear SLGS behavior.

In the last years, 2D nanomaterials, and in particular graphene, have received considerable attention, due to the wide number of demonstrated or potential applications in electronic nanodevices, energy generation and storage, biotechnologies, composite materials. The study of their mechanical behaviour plays an important role for their manufacturing and integration in devices, for tuning their performances as well as for controlling the mechanics of their composites. For this reason, considerable research efforts have been done for modelling their mechanical behaviour through a variety of approaches, ranging from the solid state physics methods to the use of equivalent continua. The most of the existing literature has focused only the in-plane behaviour of these materials, while there is a lack of studies of their transverse behaviour, relevant for buckling, wrinkling and rippling phenomena or simply to establish the bending stiffness of the continua. With this in mind, in this paper, the Gillis sticks-and-springs model for the in-plane behaviour of graphene is extended to account also for transverse deformation. To this aim, the contribution of dihedral angles is included. Numerical analyses regarding the out-of plane buckling of graphene sheets are addressed.

An atomistic based non linear analysis of single walled carbon nanotubes is proposed, as a first step for building nanoscopically informed macroscopic continuum models capable of accurately representing the system's energy associated to the atoms relative position, as well as its microscopic geometric characteristics. The arch-length method is used to solve the equilibrium equations in terms of the displacements of each Carbon atom which is seen as a material point.

The hygro-thermal behaviour of timber bridges exposed to continuously variable climates is a fundamental topic for their durability, serviceability and safety. High daily humidity variations and large moisture changes at high levels of relative humidity RH provide large moisture gradients. The use of computational hygro-thermal methods can be useful, alongside with sensor techniques, for monitoring relative humidity and temperatures in timber structures. A multi-Fickian model was previously implemented in Abaqus FEM code and verified for wooden members under Southern Europe climates. The model was able to simulate the moisture states in each point of a wooden member by using as external loads the relative humidity and temperature of the air provided by in-situ measurements or by close meteorological stations. In the present work a variant of the model is developed to take into account the higher RH variations as well as the negative temperatures in Northern Europe environments. The model is used to numerically simulate the hygro-thermal response of stress-laminated timber decks in Norwegian timber bridges.

Università degli Studi della Calabria Doctorate School of Science and Techinique "B.Telesio" Ciclo XXV, a.a. 2012

The high temperature process of wood surface densification increases the wood density in the transverse direction under compression. The recent experimental research has pointed out the influence of the process parameters on the development of the density profiles in the modified samples. The numerical modelling can help to optimize the experimental work which is often expensive due to the large amount of tests required to check the influence of the process 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 hygro-thermal equations of the problem. The relationship between the numerical profiles of moisture content and the experimental density profiles is discussed.

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 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.

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).