Narrow Results

This paper aims to develop a size-dependent numerical solution for a comprehensive study on the buckling responses of laminated functionally graded (FG) carbon nanotubes (CNTs)-reinforced composite microplates under linear and nonlinear in-plane compressive loading. According to the new modified couple stress theory and isogeometric analysis (IGA), in conjunction with the higher order plate theory, the size-dependent governing motion equations including material length scale parameter for buckling analysis of CNTs-reinforced laminated composite microplates is established. The research considers five types of loading shapes: uniform, triangular, trapezoidal, sinusoidal, and parabolic. The distribution of CNTs varies across the layer’s thickness, either uniformly or functionally patterns. The material properties of the composite layer are derived by using the New rule of mixture. The accuracy and reliability of the present solution are verified by comparing them with existing models. Different numerical examples illustrate the influences of various parameters on buckling responses of laminated FG-CNTs-reinforced composite microplates. These parameters include size-dependent effects, aspect ratio, volume fraction and distribution of CNTs, fiber orientation, lamination scheme, and boundary conditions. Additionally, the study considers a complex geometry of laminated microplates with flower cutouts to provide a comprehensive analysis.

Based on the consideration on size-dependent temperature T_m(D) where D denotes the diameter of nanoparticles and nanowires or the thickness of thin films, the size-dependent band-gap ΔE_g(D) and dielectric constant ε(D) of low dimensional materials are modeled without any adjustable parameter. The model predicts an increase of the band-gap and a decrease of dielectric constant with drop of Si nanocrystals' size. The predicted results correspond to experimental and computer simulation results of Si nanocrystals.

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

Previously it was shown that nonlocal piezoelectric differential models will lead to inconsistent bending response for Euler–Bernoulli beams under different loadings and boundary conditions. In this paper, the general strain- and stress-driven two-phase local/nonlocal integral piezoelectric models are applied to analyze the elastic buckling and free vibration of functionally graded piezoelectric (FGP) Euler–Bernoulli beams under different boundary conditions. The differential governing equations and standard boundary conditions are derived by the Hamilton’s principle. The relations between the general strain and general nonlocal stresses are expressed as integral equations, which are further transformed equivalently to differential forms with constitutive boundary conditions. Several nominal variables are introduced to simplify the differential governing and constitutive equations, as well as the standard and constitutive boundary conditions. The general differential quadrature method is applied to obtain the numerical results of buckling loads and vibration frequencies of the FGP Euler–Bernoulli beam. Numerical results show that general strain- and stress-driven two-phase local/nonlocal integral piezoelectric models will lead to consistently softening and toughening size-dependent responses, respectively.

The corotational (CR) method is effective for extending linear elements to geometrically nonlinear analysis, but faces challenges with penalty elements based on modified couple stress theory due to C¹ continuity requirements. This paper presents an alternative CR formulation for geometrically nonlinear analysis of couple stress elasticity, approximating rigid body rotation incrementally. Then, a 4-node, 12-DOF plane element US-Q4$𝜃$-CS for size-dependent materials is extended for geometrically nonlinear analysis. Numerical examples demonstrate the new nonlinear element’s excellent performance in simulating size effects for the case of geometric nonlinearity.

A size-dependent nonclassical Bernoulli–Euler beam model based on the strain gradient elasticity is proposed for piezoelectric nanowires. The governing equations and the corresponding boundary conditions are naturally derived from the variational principle. Different from the classical piezoelectric beam theory, the electric field–strain gradient coupling and the strain gradient elasticity are both taken into account. Static bending problem of a cantilever piezoelectric nanobeam is solved to illustrate the effect of strain gradient. The present model contains material length scale parameters and can capture the size dependent piezoelectricity and elasticity for nanoscale piezoelectric structures. The numerical results reveal that the deflections predicted by the present model are smaller than that by the classical beam theory and the effective electromechanical coupling coefficient is dramatic enhanced by the electric field–strain gradient coupling effect. However, the differences in both the deflections and effective EMC coefficient between the two models are very significant when the beam thickness is very small; they are diminishing with the increase of the beam thickness. This model is helpful for understanding the electromechanically coupling mechanism and in designing piezoelectric nanowires based devices.

This paper studies stress distribution in a single-walled carbon nanotube (SWCNT) under internal pressure with various chirality. Strain gradient theory is used to capture the size-dependent behavior of the SWCNT. Minimum total potential energy principle is successfully applied to derive the governing differential equation and its associated boundary conditions. Due to complexity of the governing differential equation and boundary conditions, numerical scheme is used to solve the problem. Comparing the results based on strain gradient theory and that of classical elasticity shows a major difference between these two methods. However, a close examination of the results indicates that both theories predict the same trend for variations in the radial displacement along the SWCNT radius. Numerical results also indicate that the proposed model can lead into the classical elasticity model, provided the material length scale parameters are taken to be zero. Additionally, for plane strain condition, the radial displacements predicted by strain gradient theory are lower than those predicted by classical elasticity theory. Moreover, numerical results show that in a SWCNT, the non-dimensional radial and circumferential stresses along the wall thickness of the SWCNT increase as the radius is increased. The opposite behavior is true for non-dimensional high-order stresses.

Studying the thermodynamic properties of the reaction of nanoparticle with organic substance is significant for the application of nanomaterial in organic fields. In this work, by using the reaction of nano-ZnO with different particle sizes with benzoic acid as a research system, the size-dependent standard equilibrium constant and reaction thermodynamic properties were analyzed theoretically, and the influence regularities of the particle size on the standard equilibrium constant and the reaction thermodynamic properties were studied. The excellent agreement between the experimental results and theoretical analysis shows that the particle size has remarkable influence on the standard equilibrium constant and the thermodynamic properties of the reaction; with the decrease of the particle size, the standard equilibrium constant increases, while the standard molar reaction Gibbs energy, the standard molar reaction enthalpy and the standard molar reaction entropy decrease. Furthermore, the logarithm of the standard equilibrium constant and the thermodynamic properties present linear relations with the reciprocal of the particle diameter, respectively. The theory and the influence regularities will provide useful tools to lead better and broader application of nanomaterial in organic fields.

Zinc oxide nanoparticles (ZnO NPs) are widely used in diverse fields. However, the toxicological effects of ZnO NPs remain inadequately explored. This study aimed to investigate the toxicities of various concentrations of ZnO NPs <50 nm (ZnO NP50), <100 nm (ZnO NP100), and ZnO bulk particles (ZnO BP) after different exposure durations using Caenorhabditis elegans (C. elegans) as an in vivo model, focusing on reproductive capacity, feeding behavior, and lifespan. Polymerase chain reaction (PCR) was conducted to assess expressions of stress-related cep-1 and pmk-1 genes. The results revealed that the effects of ZnO particles on C. elegans’ reproductive capacity were inconsistent after exposure for 24, 48, and 72 h. It was seen a general concentration-dependent reduction in pharyngeal pumping rate, with 1000$\mu$g/mL having the most significant impact across all ZnO particle treatments. Lifespan studies showed no significant differences post exposure of ZnO particles for the mean lifespan of C. elegans, while significant differences for ZnO NP50 treatment at 100$\mu$g/mL and 1000$\mu$g/mL compared to the control and the ZnO BP groups were observed. Finally, PCR results suggested significant up-regulation of cep-1 and pmk-1 gene expression, showing a size-dependent linear trend with ZnO NP50 > ZnO NP100 > ZnO BP. In conclusion, this study underscores the complex size-dependent toxicological effects of ZnO NPs on C. elegans, highlighting significant impacts on pharyngeal pumping rate and gene expression profiles associated with stress response and DNA damage repair pathways. These findings contribute to our understanding of NP toxicity and underscore the importance of size, concentration, and exposure duration considerations in assessing their biological effects.