Minh-Quy Le’s research while affiliated with Hanoi University of Science and Technology and other places

In this article, the effects of temperature and size-dependent on the buckling behavior of functionally graded (FG) cylindrical nanopanels resting on elastic foundation using nonlocal strain gradient theory are investigated in detail analytical approach. According to a simple power-law distribution, the material properties of FG cylindrical nanopanels are assumed to vary continuously through the thickness direction. The Pasternak model is used to describe the reaction of the elastic foundation on the FG cylindrical nanopanels. The fundamental relations and stability equations are derived by applying the nonlocal strain gradient theory and the classical shell theory based on the adjacent equilibrium criterion. Using Galerkin's method, the mechanical buckling behavior of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment is solved. The reliability of the obtained results has been verified by comparison with the previous results in the literature. Based on the obtained results, the influences of the material length scale parameter, the nonlocal parameter, temperature increment, geometric parameters, material properties, and elastic foundation on buckling behaviors of FG cylindrical nanopanels resting on an elastic foundation in the thermal environment are analyzed and discussed.

Nodal stresses are exploited in peridynamics to investigate the mode-I J-integral of single edge- and center-cracked plates with initial crack length-plate width ratios from 0.1 through 0.5. Computed values of the J-integral on six different contours differ from each other by about 1% and are compared and discussed with analytical methods, with finite element analysis as well as with previous peridynamic studies. Simulation results show that mode-I J-integral via peridynamic stresses are highly accurate.

In linear elastic fracture mechanics, the critical stress intensity factor (CSIF) is related to the surface energy calculated from the bond energy in the reference configuration. For nanomaterials, the difference between the thus computed CSIF and that found from other methods is attributed to lattice trapping. We show here that the energy release rate (and hence the CSIF) determined from the energy of bonds on the crack surface in the current configuration agrees with that estimated by the traditional methods employing the fracture stress and the initial crack length. We demonstrate this by using molecular dynamics simulations with the Tersoff potential by studying crack propagation in a pre-cracked monolayer boronitrene.

The fracture toughness has been theoretically and experimentally estimated for few of various two-dimensional (2D) materials. Relationship between the fracture toughness and other mechanical properties of 2D hexagonal materials is extremely needed for a quick estimation in engineering applications, as well as for a better comprehension of their fracture properties. The present work investigates through molecular dynamics simulations at room temperature the mode-I fracture of 25 single-atom-thick hexagonal materials with the buckling height-bond length ratio in the range from 0 through ∼0.6, including 6 planar sheets (graphene, boronitrene, SiC, GeC, AlN and InN) and 19 buckled sheets (silicene, InP, SiGe, SnSi, SnGe, SnO, GeO, SiO, blue-P, arsenene, GeS, SnS, antimonene, bismuthene, SiTe, SnSe, SiSe, GeTe and SnTe). Fracture mechanism is considered. With this large data set and based on dimensional analysis, an empirical formula is established to estimate the mode-I fracture toughness from the elastic modulus, intrinsic tensile strength, bond length and buckling height of a single-atom-thick hexagonal material with reasonable accuracy. This simple formula provides quick estimation of the fracture toughness and is useful for engineering applications.

Mode-I stress intensity factors are estimated for 28 buckled two-dimensional hexagonal materials, including 6 mono-elemental (silicene, indiene, blue phosphorene, arsenene, antimonene and bismuthene) and 22 binary (CS, CSe, CTe, SiO, SiS, SiSe, SiTe, SiGe, GeO, GeS, GeSe, GeTe, SnO, SnS, SnSe, SnTe, SnGe, SnSi, InAs, InSb, GaAs and AlSb) two-dimensional materials. The crack-tip displacement field revealed from linear elastic fracture mechanics is adopted to find the stress intensity factor. Atomic-scale finite element method with Stillinger-Weber potentials is used to simulate the tensile tests. Mode-I stress intensity factors of these 28 two-dimensional materials appear ≤ 0.8 MPam, which are very small in comparison with boronitrene and graphene. Most of them exhibit their fracture toughness below 0.5 MPam. Our findings are helpful in the design of nano-devices with these two-dimensional materials.

The nonlinear vibration of a nanobeam under electrostatic force is investigated through the nonlocal strain gradient theory. Using Galerkin method, the partial differential equation of motion is reduced to an ordinary nonlinear differential one. The equivalent linearization method with a weighted averaging and a variational approach are used independently to establish the frequency–amplitude relationship under closed-forms for comparison purpose. Effects of material and operational parameters on the frequency ratio (the ratio of nonlinear frequency to linear frequency), on the nonlinear frequency, and on the stable configuration of the nanobeam are studied and discussed.

We study through extensive finite element analysis the lithium diffusion in small elements of Si anodes under the forms of spheres, rods and circular disks for Li-ion batteries. Elastoplastic properties of the amorphous silicon are assumed to be lithium concentration-dependent. Effects of the normalized flux of Li-ions on the lithium concentrations, stresses and total equivalent plastic strains are considered. Effects of the disk's thickness are also included. At a given normalized flux, the heterogeneity of the lithiation, stresses and plastic deformation increase in the order: disk, sphere and rod. The thinner disk the better performance is. Below a critical value of the normalized flux of Li-ions, silicon spheres and disks exhibit linear elasticity and homogeneous distribution of Li-ions, whereas silicon rods undergo always plastic deformation after lithiation. When the radii of these 3 structures are smaller than several micrometers and the normalized flux is taken as 95% of their critical value, the charge time falls in the range from minutes to several hours. Our findings will help to optimize the charge and geometrical parameters for silicon anodes.

We investigate the nonlinear vibration of microbeams based on the nonlinear elastic foundation through the modified couple stress theory. The equivalent linearization method with a weighted averaging is used to solve approximately the ordinary differential equation that describes the equation of motion of the microbeam. The effects of length scale parameter, the flexural rigidity ratio, the slenderness ratio, the Winkler parameter, the Pasternak parameter and the nonlinear foundation parameter on the nonlinear vibration of the microbeam are studied and discussed.