Nataliya A. Sakharova

Group 13–phosphide nanosheets and nanotubes represent a family of nanostructures whose mechanical properties remain unevenly explored, particularly across the complete B–Al–Ga–In–Tl series. In this work, the elastic behavior of boron phosphide, aluminum phosphide, gallium phosphide, indium phosphide and thallium phosphide nanosheets and single-walled nanotubes is systematically investigated using nanoscale continuum modeling based on molecular structural mechanics and finite element analysis. The surface Young’s and shear moduli of the nanosheets are evaluated and their variation along the group 13–phosphide series is analyzed. The corresponding nanotubes are investigated considering zigzag, armchair and chiral configurations with diameters above 1.3 nm to assess the influence of geometry and chirality on their elastic response. The results reveal an overall decrease in the elastic properties along the B–Al–Ga–In–Tl series, although the trend is not uniform for all compounds and properties. The surface Young’s moduli of the nanotubes are found to be comparable to those of the corresponding nanosheets, whereas their surface shear moduli are consistently higher, despite the different deformation modes involved. Overall, this study provides a consistent assessment of the mechanical behavior of both 2D and 1D group 13–phosphide nanostructures within a unified modeling framework, while also providing reference data for compounds whose elastic properties remain scarcely reported.

Non-carbon nanotubes are attractive nanostructures with potential applications in advanced electronic and high-temperature devices. Among boron–group 15 nanotubes, boron nitride nanotubes (BNNTs) have been extensively investigated, whereas the mechanical behaviour of boron phosphide (BPNTs), boron arsenide (BAsNTs) and boron antimonide (BSbNTs) nanotubes remains considerably less explored, particularly for the latter two compounds. A systematic comparative investigation of linear elastic behaviour was carried out for single-walled BNNTs, BPNTs, BAsNTs and BSbNTs over a wide range of diameters using the nanoscale continuum modelling/molecular structural mechanics (NCM/MSM) approach. Tensile, bending and torsional rigidities, surface Young’s and shear moduli, and Poisson’s ratio were assessed, and analytical expressions for their evaluation were proposed. The results were discussed in terms of nanotube diameter, chirality and equilibrium bond length, with particular attention to the influence of the group 15 atoms. Comparisons with available literature data and the previously investigated group 13–nitride nanotube family were used to identify common and distinct trends. Within the adopted modelling framework, the results provide a consistent description of elastic behaviour across the entire boron–group 15 nanotube family and reveal comparative trends that can guide further theoretical and computational studies.

It is expected that two-dimensional (2D) metal nitrides (MNs) consisting of the 13th group elements of the periodic table and nitrogen, namely aluminium nitride (AlN), gallium nitride (GaN), indium nitride (InN) and thallium nitride (TlN), have enhanced physical and mechanical properties due to the honeycomb, graphene-like atomic arrangement characteristic of these compounds. The basis for the correct design and improved performance of nanodevices and complex structures based on 2D MNs from the 13th group is an understanding of the mechanical response of their components. In this context, a comparative study to determine the elastic properties of metal nitride nanosheets was carried out making use of the nanoscale continuum modelling (or molecular structural mechanics) method. The differences in the elastic properties (surface shear and Young’s moduli and Poisson’s ratio) found for the 2D 13th group MNs are attributed to the bond length of the respective hexagonal lattice of their diatomic nanostructure. The outcomes obtained contribute to a benchmark in the evaluation of the mechanical properties of AlN, GaN, InN and TlN monolayers using analytical and numerical approaches.

It is expected that two-dimensional (2D) metal nitrides (MNs), consisting of the elements of the 13th group of the periodic table and nitrogen, namely aluminium nitride (AlN), gallium nitride (GaN), indium nitride (InN) and thallium nitride (TlN) have enhanced physical and mechanical properties, due to a honeycomb graphene-like atomic arrangement, characteristic to these compounds. The basis for the correct design and improved performance of nanodevices and complex structures based on 2D MNs of the 13th group is the understanding of the mechanical response of their components. In this context, a comparative study to determine the elastic properties of metal nitride nanosheets was carried out making use of the nanoscale continuum modelling (or molecular structural mechanics) method. The differences in the elastic properties (surface Young´s and shear moduli, and Poisson´s ratio) found for 2D 13th group MNs are attributed to the bond length of the respective diatomic hexagonal lattice. The results obtained contribute to a benchmark in the evaluation of mechanical properties of AlN, GaN, InN and TlN monolayers by analytical and numerical approaches.

In recent years, tubular nanostructures have been related to immense advances in various fields of science and technology. Considerable research efforts have been centred on the theoretical prediction and manufacturing of non-carbon nanotubes (NTs), which meet modern requirements for the development of novel devices and systems. In this context, diatomic inorganic nanotubes formed by atoms of elements from the 13th group of the periodic table (B, Al, Ga, In, Tl) and nitrogen (N) have received much research attention. In this study, the elastic properties of single-walled boron nitride, aluminium nitride, gallium nitride, indium nitride, and thallium nitride nanotubes were assessed numerically using the nanoscale continuum modelling approach (also called molecular structural mechanics). The elastic properties (rigidities, surface Young’s and shear moduli, and Poisson’s ratio) of nitride nanotubes are discussed with respect to the bond length of the corresponding diatomic hexagonal lattice. The results obtained contribute to a better understanding of the mechanical response of nitride compound-based nanotubes, covering a broad range, from the well-studied boron nitride NTs to the hypothetical thallium nitride NTs.

In the recent years, tubular nanostructures have been related with immense advances in various fields of science and technology. Considerable research efforts have been centered on the theoretical prediction and manufacturing of non-carbon nanotubes (NTs), which meet modern requirements for the developing of novel devices and systems. In this context, diatomic inorganic nanotubes formed by atoms of elements from the 13th group of the periodic table (B, Al, Ga, In, Tl) and nitrogen (N), have received much research attention. In the present work, the elastic properties of single-walled boron nitride, aluminium nitride, gallium nitride, indium nitride and thallium nitride nanotubes were numerically evaluated using the nanoscale continuum modelling approach (also called molecular structural mechanics). The elastic properties (rigidities, surface Young´s and shear moduli, and Poisson´s ratio) of nitride nanotubes are discussed with respect to the bond length of the corresponding diatomic hexagonal lattice. The results obtained contribute to a better understanding of the mechanical response of nitride compound-based nanotubes, covering a broad range from the well-studied boron nitride NTs to the hypothetical thallium nitride NTs.

This study investigates the sensitivity of the square cup forming process. It analyses how the uncertainties in the material properties, friction and process conditions affect the results of the square cup, such as equivalent plastic strain, geometry change, thickness reduction, punch force and springback. The cup flange and the die curvature region are identified as highly affected areas, while the cup bottom is least affected by the uncertainties. Two sensitivity analysis techniques, PAWN and Sobol indices, are compared. In particular, the study shows that PAWN indices require a significantly smaller number of simulations than Sobol indices, making them a more efficient choice for sensitivity analysis. While both PAWN and Sobol indices generally give comparable results, discrepancies arise in the analysis of springback, where PAWN indices show superior accuracy, particularly when dealing with multimodal distributions. This observation highlights the importance of selecting the appropriate sensitivity analysis method based on the nature of the data being analysed. These results provide insights for optimizing stamping processes to reduce production time and costs.

An identification strategy based on a machine learning approach is proposed to identify the constitutive parameters of metal sheets. The main novelty lies in the use of Gaussian Process Regression with the objective of identifying the constitutive parameters of metal sheets from the biaxial tensile test results on a cruciform specimen. The metamodel is intended to identify the constitutive parameters of the work hardening law and yield criterion. The metamodel used as input data the forces along both arms of the cruciform specimen and the strains measured for a given set of points. The identification strategy was tested for a wide range of virtual materials, and it was concluded that the strategy is able to identify the constitutive parameter with a relative error below to 1%. Afterwards, an uncertainty analysis is conducted by introducing noise to the force and strain measurements. The optimal strategy is able to identify the constitutive parameters with errors inferior to 6% in the description of the hardening, anisotropy coefficients and yield stresses in the presence of noise. The study emphasizes that the main strength of the proposed strategy relies on the judicious selection of critical areas for strain measurement, thereby increasing the accuracy and reliability of the identification process.

Two-dimensional (2D) nanostructures of aluminum nitride (AlN) and gallium nitride (GaN), called nanosheets, have a graphene-like atomic arrangement and represent novel materials with important upcoming applications in the fields of flexible electronics, optoelectronics, and strain engineering, among others. Knowledge of their mechanical behavior is key to the correct design and enhanced functioning of advanced 2D devices and systems based on aluminum nitride and gallium nitride nanosheets. With this background, the surface Young’s and shear moduli of AlN and GaN nanosheets over a wide range of aspect ratios were assessed using the nanoscale continuum model (NCM), also known as the molecular structural mechanics (MSM) approach. The NCM/MSM approach uses elastic beam elements to represent interatomic bonds and allows the elastic moduli of nanosheets to be evaluated in a simple way. The surface Young’s and shear moduli calculated in the current study contribute to building a reference for the evaluation of the elastic moduli of AlN and GaN nanosheets using the theoretical method. The results show that an analytical methodology can be used to assess the Young’s and shear moduli of aluminum nitride and gallium nitride nanosheets without the need for numerical simulation. An exploratory study was performed to adjust the input parameters of the numerical simulation, which led to good agreement with the results of elastic moduli available in the literature. The limitations of this method are also discussed.

Among the compounds formed by an element of the 13th group and nitrogen, boron nitride, also called white graphene, stands out for its high strength and thermal conductivity, transparency to visible light, antimicrobial properties, high resistance to oxidation, and biocompatibility. One-dimensional and two-dimensional boron nitride nanostructures, i.e. nanotubes and nanosheets, respectively, are expected to present innovative advanced characteristics not equal to those of bulk boron nitride, bringing new perspectives to numerous applications in nanoscale electronics and biomedicine. For the correct design of systems and devices consisting of boron nitride nanosheets and nanotubes, understanding the mechanical behaviour of these nanostructures is extremely important. Firstly, because the robustness and functioning of nanosystems and nanodevices based on boron nitride nanostructures are determined by the mechanical behaviour of their constituents and also because deformation can influence the optical, electric, and thermoelectric properties of boron nitride nanotubes and nanosheets. In this context, the current chapter is dedicated to the numerical evaluation of the elastic properties of boron nitride nanosheets and nanotubes, using the nanoscale continuum modelling (also called molecular structural mechanics) approach. With this aim, a three-dimensional finite element model was used to evaluate their elastic moduli.