Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory.

Microtubules including tubulin heterodimers arranging in a parallel shape of cylindrical hollow plays an important role in the mechanical stiffness of a living cell. In the present study, the nonlocal strain gradient theory of elasticity including simultaneously the both nonlocality and strain gradient size dependency is put to use within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation to analyze the size-dependent buckling and postbuckling characteristics of microtubules embedded in cytoplasm under axial compressive load. The non-classical governing differential equations are deduced via boundary layer theory of shell buckling incorporating the nonlinear prebuckling deformation and microtubule-cytoplasm interaction in the living cell environment. Finally, with the aid of a two-stepped perturbation solution methodology, the explicit analytical expressions for nonlocal strain gradient stability paths of axially loaded microtubules are achieved. It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them.

Micromechanical modeling of rate-dependent behavior of Connective tissues.

In this paper, a constitutive and micromechanical model for prediction of rate-dependent behavior of connective tissues (CTs) is presented. Connective tissues are considered as nonlinear viscoelastic material. The rate-dependent behavior of CTs is incorporated into model using the well-known quasi-linear viscoelasticity (QLV) theory. A planar wavy representative volume element (RVE) is considered based on the tissue microstructure histological evidences. The presented model parameters are identified based on the available experiments in the literature. The presented constitutive model introduced to ABAQUS by means of UMAT subroutine. Results show that, monotonic uniaxial test predictions of the presented model at different strain rates for rat tail tendon (RTT) and human patellar tendon (HPT) are in good agreement with experimental data. Results of incremental stress-relaxation test are also presented to investigate both instantaneous and viscoelastic behavior of connective tissues.

Nonlocal strain gradient beam model for postbuckling and associated vibrational response of lipid supramolecular protein micro/nano-tubules.

As a supramolecular construction, lipid protein micro/nano-tubules can be utilized in a variety of sustained biological delivery system. The high slenderness ratio of lipid tubules makes their hierarchical assembly into a desired architecture difficult. Therefore, an accurate prediction of mechanical behavior of lipid tubular is essential. The objective of this study is to capture size dependency in the postbuckling and vibrational response of the postbuckled lipid micro/nano-tubules more comprehensively. To this purpose, the nonlocal strain gradient elasticity theory is incorporated to the third-order shear deformation beam theory to develop an unconventional beam model. Hamilton's principle is put to use to establish the size-dependent governing differential equations of motion. After that, an improved perturbation technique in conjunction with Galerkin method is employed to obtain the nonlocal strain gradient load-frequency response and postbuckling stability curves of lipid micro/nano-tubules. It is revealed that by taking the nonlocal size effect into consideration, the influence of the type (geometrical parameters) of an axially compressed lipid micro/nano-tubule on its natural frequency in order decreases and increases within the prebuckling and postbuckling regimes. While the strain gradient size dependency plays an opposite role which causes that the influence of the type of lipid micro/nano-tubule on its natural frequency corresponding to the prebuckling and postbuckling domains increases and decreases, respectively.

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.

An efficient size-dependent shear deformable shell model and molecular dynamics simulation for axial instability analysis of silicon nanoshells.

Understanding the size-dependent behavior of structures at nanoscale is essential in order to have an effective design of nanosystems. In the current investigation, the surface elasticity theory is extended to study the nonlinear buckling and postbuckling response of axially loaded silicon cylindrical naoshells. Thereby, an efficient size-dependent shear deformable shell model is developed including the size effect of surface free energy. A boundary layer theory of shell buckling in conjunction with a perturbation-based solution methodology is employed to predict the size dependency in the buckling loads and postbuckling behavior of silicon nanoshells having various thicknesses. After that, on the basis of the Tersoff empirical potential, a molecular dynamics (MD) simulation is performed for a silicon cylindrical nanoshell with thickness of four times of silicon lattice constant, the critical buckling load and critical shortening of which are extracted and compared with those of the developed non-classical shell model. It is demonstrated that by taking the effects of surface free energy into account, a very good agreement is achieved between the results of the developed size-dependent continuum shell model and those of MD simulation.

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

The unique geometry with high surface ratio makes lipid micro/nano-tubules as an excellent self-assembled supramolecular structure in various biological applications such as controllable release systems and drug delivery. In the present study, the size-dependent nonlinear vibrations of axially loaded lipid micro/nano tubules associated with the both prebuckling and postbuckling domains are explored comprehensively. To accomplish this purpose, the nonlocal strain gradient theory of elasticity including simultaneously two entirely different features of size dependency is utilized within the framework of the third-order shear deformable beam model. With the aid of Hamilton's principle, the non-classical governing differential equations of motion are established incorporating the nonlinear prebuckling deformations and the large postbuckling deflections. At the end, the Galerkin method in conjunction with an improved perturbation technique is employed to initiate explicit analytical expressions for nonlocal strain gradient nonlinear frequency of pre- and post-buckled lipid micro/nano-tubules. It is seen that by taking the nonlocal size effect into consideration, the influence of geometrical parameters of the lipid micro/nano-tubule on the nonlinear vibration characteristics within the both prebuckling and postbuckling domains decreases and the frequency-deflection curves are more close to each other. However, the strain gradient size dependency has an opposite effect and leads to increase the gap between the frequency-deflection curves of axially compressed lipid micro/nano-tubules with different geometrical parameters.

Micromechanics and constitutive modeling of connective soft tissues.

In this paper, a micromechanical model for connective soft tissues based on the available histological evidences is developed. The proposed model constituents i.e. collagen fibers and ground matrix are considered as hyperelastic materials. The matrix material is assumed to be isotropic Neo-Hookean while the collagen fibers are considered to be transversely isotropic hyperelastic. In order to take into account the effects of tissue structure in lower scales on the macroscopic behavior of tissue, a strain energy density function (SEDF) is developed for collagen fibers based on tissue hierarchical structure. Macroscopic response and properties of tissue are obtained using the numerical homogenization method with the help of ABAQUS software. The periodic boundary conditions and the proposed constitutive models are implemented into ABAQUS using the DISP and the UMAT subroutines, respectively. The existence of the solution and stable material behavior of proposed constitutive model for collagen fibers are investigated based on the poly-convexity condition. Results of the presented micromechanics model for connective tissues are compared and validated with available experimental data. Effects of geometrical and material parameters variation at microscale on macroscopic mechanical behavior of tissues are investigated. The results show that decrease in collagen content of the connective tissues like the tendon due to diseases leads 20% more stretch than healthy tissue under the same load which can results in connective tissue malfunction and hypermobility in joints.