Nonlinear vibrations of pre- and post-buckled lipid supramolecular micro/nano-tubules via nonlocal strain gradient elasticity theory

Mechanics of Small-Scale Spherical Inclusions Using Nonlocal Poroelasticity Integrated with Light Gradient Boosting Machine

Detecting inclusions in materials at small scales is of high importance to ensure the quality, structural integrity and performance efficiency of microelectromechanical machines and products. Ultrasound waves are commonly used as a non-destructive method to find inclusions or structural flaws in a material. Mathematical continuum models can be used to enable ultrasound techniques to provide quantitative information about the change in the mechanical properties due to the presence of inclusions. In this paper, a nonlocal size-dependent poroelasticity model integrated with machine learning is developed for the description of the mechanical behaviour of spherical inclusions under uniform radial compression. The scale effects on fluid pressure and radial displacement are captured using Eringen's theory of nonlocality. The conservation of mass law is utilised for both the solid matrix and fluid content of the poroelastic material to derive the storage equation. The governing differential equations are derived by decoupling the equilibrium equation and effective stress-strain relations in the spherical coordinate system. An accurate numerical solution is obtained using the Galerkin discretisation technique and a precise integration method. A Dormand-Prince solution is also developed for comparison purposes. A light gradient boosting machine learning model in conjunction with the nonlocal model is used to extract the pattern of changes in the mechanical response of the poroelastic inclusion. The optimised hyperparameters are calculated by a grid search cross validation. The modelling estimation power is enhanced by considering nonlocal effects and applying machine learning processes, facilitating the detection of ultrasmall inclusions within a poroelastic medium at micro/nanoscales.

Improved perturbation solution for two-dimensional viscous flow between expanding or contracting permeable walls

Despite the continuing interest in the transport of biological fluid within contracting or expanding vessels, our knowledge is yet to be fully developed, even in the two-dimensional case. For example, explicit solutions and close approximations to these models remain unknown, and the physical problem has been restricted to the "slow" expansion or contraction of the walls. Thus, the purpose of this short communication is to partially address such challenges and gaps by generating explicit solutions and improving approximations to the flow problem without the "slowness" restriction being imposed. We show that when the Reynolds number is zero (i.e., the inviscid case), the corresponding homogeneous differential equation under consideration may be completely solved. We then illustrate how this exact solution may be leveraged to form more precise approximations to the flow via perturbation techniques when the Reynolds number is small. Our perturbation approach is only in one parameter (the Reynolds number) instead of the usual two parameters (the Reynolds number and wall dilation rate), and thus we make no restriction regarding the "slowness" of wall expansion or contraction for our general perturbation scheme. Our act of "shining new light through old windows" improves and extends the results of Majdalani, Zhou and Dawson and, moreover, our method has significant potential to be applied by researchers to form more precise one-parameter perturbation approximations to flow problems in contrast to the limitations of the traditional two-parameter perturbation approaches that have dominated the literature.

Size-dependent thermo-mechanical vibration of lipid supramolecular nano-tubules via nonlocal strain gradient Timoshenko beam theory

Nowadays, nanostructured lipid carriers are used as carrier systems to control the release of drug molecules and promote their physicochemical stability. A better understanding of the dynamic behavior of lipid nano-tubules can facilitate a better drug delivery and other relevant applications. The dynamic behaviors of these lipid nano-tubules are susceptible to temperature variations. Hence, a deeper insight into these effects, as mentioned above, is necessary to ensure higher analysis efficiency. However, the models used in previous researches did not take into account these effects. The lipid nano-tubules often possess a small length-to-width ratio and as a result, the use of the Euler-Bernoulli beam theory for modeling them will significantly reduce the accuracy of calculations, in which Timoshenko beam model is used to increase the accuracy of the model. The main objective of the current study is to investigate the bending vibrations of lipid nano-tubules by considering the temperature effects based on nonlocal strain gradient theory. To this end, based on Hamilton's principle, the governing equations of a dynamical system were extracted by taking into account the temperature effects. The equations were solved using the Navier solution method. Moreover, the dimensionless natural frequency and critical temperature of the lipid nano-tubules were calculated. Our findings demonstrate that the critical temperature is a function of the nonlocal parameter and length-scale parameter variations. It is also observed that at a certain interval of the length scale parameter, increasing the value of the nonlocal parameter results in intensification of the hardening behavior of lipid nano-tubules. Based on our findings, the proposed model indicates good accuracy and prediction.

Advances in modelling and analysis of nano structures: a review

Nanostructures are widely used in nano and micro-sized systems and devices such as biosensors, nano actuators, nano-probes, and nano-electro-mechanical systems. The complete understanding of the mechanical behavior of nanostructures is crucial for the design of nanodevices and systems. Therefore, the flexural, stability and vibration analysis of various nanostructures such as nanowires, nanotubes, nanobeams, nanoplates, graphene sheets and nanoshells has received a great attention in recent years. The focus has been made, to present the structural analysis of nanostructures under thermo-magneto-electro-mechanical loadings under various boundary and environmental conditions. This paper also provides an overview of analytical modeling methods, fabrication procedures, key challenges and future scopes of development in the direction of analysis of such structures, which will be helpful for appropriate design and analysis of nanodevices for the application in the various fields of nanotechnology.

Influence of MgO nanoparticles on the mechanical properties of coated hydroxyapatite nanocomposite scaffolds produced via space holder technique: Fabrication, characterization and simulation

In the current study, hydroxyapatite (HA)-MgO scaffolds are fabricated with the aid of the space holder technique using NaCl as the spacer type. After that, the fabricated samples are deposited in gelatin (GN) with ibuprofen (IBO) substitution to create GN-IBO thin surface coating. The samples are then synthesized chemically and the associated properties are studied using X-ray diffraction (XRD) and scan electron microscopy (SEM) equipped with the energy dispersive spectroscopy (EDS). The compressive strength, fracture toughness, hardness, porosity, bioactivity, degradation rate, wettability, and roughness of the manufactured HA-MgO bio-nanocomposite scaffolds containing different weight fractions of MgO nanoparticles are predicted. Accordingly, nonlinear mechanical behaviors including nonlinear free vibration and nonlinear vibrations associated with the prebuckling and postbuckling domains of an axially loaded plate-type bone implant made of the HA-MgO bio-nanocomposites coated with the GN-IBO thin layers are investigated analytically via a sandwich plate model. The obtained results reveal that magnesium has no considerable effect on the porosity, however it causes to enhance the compressive strength significantly. The presence of magnesium ions also leads to reduce the crystallinity of HA about 30-100 nm due to entering MgO nanoparticles into the network. The results related to the sample with 10 wt% MgO nanoparticles indicate that the microscopic structure of the fabricated bio-nanocomposite scaffold is three-dimensional with porous architecture. Also, it is shown that the solubility of the HA composed with MgO nanoparticles decreases with higher bioactivity.

Mechanical and biological performance of axially loaded novel bio-nanocomposite sandwich plate-type implant coated by biological polymer thin film

Post-surgical infection is one of the essential problems in bone scaffolds that is usually treated with antibiotics. This issue may be related to the poor blood supply for bone tissue due to high concentrations of drug. In the current study, the effect of zinc oxide (ZnO) nanoparticles on the antibacterial behavior of the nanocrystalline hydroxyapatite (n-HA) scaffolds coated by gelatin-ibuprofen (GN-IBO) is evaluated. To this end, the bio-nanocomposite scaffolds are fabricated via the space holder technique and then characterized with the aid of X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). The compressive strength, fracture toughness, porosity, elastic modulus as the mechanical properties, and the apatite formation, biodegradation, drug release and wettability beside the roughness as the biological properties are predicted. The obtained experimental results indicate that the bio-nanocomposite scaffolds containing 10 wt% ZnO has suitable mechanical and biological properties. After that, an analytical model is developed to predict the nonlinear instability and vibration responses of an axially loaded sandwich plate-type implants made of the fabricated n-HA-ZnO bio-nanocomposites coated by GN-IBO thin film corresponding to various weight fractions of ZnO nanoparticles. It is found that ZnO peaks in the positions of 2θ are equal to 31.6°, 33.6°, 34°, 46.4°, and 62°, which represent the crystalline characteristics. Also, it is revealed that through addition of ZnO nanoparticles, the hardness and elastic modulus as well as the bone formation and biodegradation rate of the bio-nanocomposite scaffold enhance, while its drug release in the phosphate buffer solution detected with UV spectrum reduces. It is found that by increasing the ZnO weight fraction, the critical axial buckling load of the sandwich bio-nanocomposite implant enhances, and it buckles at lower axial shortening. However, it is seen that for higher value of wt% ZnO, its influence on the critical buckling load decreases.