Size-dependent Material Properties Research Articles

Identifying structure-property relationships of micro-architectured porous scaffolds through 3D printing and finite element analysis

This study integrates 3D printing and finite element analysis (FEA) to investigate the effect of micro-architectural characteristics on the mechanical properties of porous scaffolds. The studied characteristics include the thickness of the scaffold walls and the number of domains at the cross-section. We use 3D printing to fabricate scaffolds of deliberately designed microstructures to enable strict architecture control of the scaffolds. The longitudinal compressive properties of different scaffolds are first analyzed through experimental testing. Then, FEA is conducted to investigate the mechanical properties and the deformation mechanisms of the scaffolds. We find that decreasing wall thickness leads to failure mechanism transition from wall compression failure to buckling instability. For scaffolds with different wall thicknesses, the failure mechanisms and the critical loads are evaluated using the theory of thin plate buckling. For the characteristic of the number of domains, both experimental and FEA results show increasing effective stiffness with increasing domains. Interestingly, we find that with the material properties extracted from a single wall scaffold, the computational models tend to overestimate the effective compression modulus of scaffolds with larger numbers of walls or domains than the experimental data. This observation indicates possible size-dependent material properties in 3D printed structs. Our study demonstrates that integrating experiments and computational modeling can provide fundamental insights into the mechanical properties and deformation mechanisms of micro-architectured scaffolds and unveil unique small-scale material behaviors.

Wave dispersion characteristics in lipid tubules considering shell model based on nonlocal strain gradient theory

In this paper, wave dispersion analysis of lipid tubules is presented by using the first-order shear deformation (FSD) shell theory. The small-scale effect is revealed explicitly based on the nonlocal strain gradient theory (NSGT). Different types of lipid tubules with size-dependent material properties are taken into account. Hamilton’s principle is utilized to derive the equations of wave motion. The analytical solutions of phase velocity and wave frequency of propagated waves are obtained. In addition, detailed investigations are implemented to highlight the effects of the types of lipid tubules, the longitudinal and circumferential wave numbers, the material length scale parameters and the nonlocal parameters on the wave dispersion characteristics of lipid tubules.

Harmonic response of carbon nanotube reinforced functionally graded beam by finite element method

Abstract This paper examines the harmonic response of carbon nanotube (CNT) reinforced functionally graded beams. Two different varieties of CNT reinforced composite beams are considered. One is of uniform distribution CNT reinforced composite and the other is functionally graded CNT reinforced beam. As the general rule of mixture is not appropriate for such beams, another rule of mixture is applied to obtain material properties. For these beams, CNT efficiency parameter is taken for the size dependent material properties. Finite element models are generated for the beams in the ANSYS environment using the computed material properties. Three different kinds of FG beams, functionally graded CNT beams of X type (FG X -CNT), Δ type (FGΔ-CNT) and O type are taken for evaluation and presentation of results. It is found that the FGΔ-CNT reinforced composite beams have maximum amplitude peak. This maximum peak of rotational motion belongs to FGO-CNT reinforced composite beams and FGO CNT has more stability than the other. The FGX CNT reinforced composite beams have the highest natural frequency with low peak and thereby explaining small hardening behavior.

Multiscale Modeling of Fiber Fragmentation Process in Aligned ZnO Nanowires Enhanced Single Fiber Composites

A three-dimensional multiscale modeling framework is developed to analyze the failure procedure of radially aligned zinc oxide (ZnO) enhanced single fiber composites (SFC) under tensile loading to understand the interfacial improvement between the fiber and the matrix. The model introduces four levels in the computational domain. The nanoscale analysis calculates the size-dependent material properties of ZnO nanowires. The interaction between ZnO nanowires and the matrix is simulated using a properly designed representative volume element at the microscale. At the mesoscale, the interface between the carbon fiber and the surrounding area is modeled using the cohesive zone approach. A combination of ABAQUS Finite element software and the failure criteria modeled in UMAT user subroutine is implemented to simulate the single fiber fragmentation test (SFFT) at the macroscale. The numerical results indicate that the interfacial shear strength of SFC can be improved up to 99% after growing ZnO nanowires on the fiber. The effect of ZnO nanowires geometries on the interfacial shear strength of the enhanced SFC is also investigated. Experimental ZnO nanowires enhanced SFFTs are performed on the fabricated samples to validate the results of the developed multiscale model. A good agreement between the numerical and the experimental results was observed.

Size-dependent instability of organic solar cell resting on Winkler–Pasternak elastic foundation based on the modified strain gradient theory

The present study employs the modified strain gradient theory (MSGT) in conjunction with the refined shear deformation plate theory to explore the buckling behaviour of simply supported and clamped OSC. The Winkler-Pasternak elastic foundation is implemented to idealise the foundation. The size-dependent effect of the OSC is captured by the three length scale parameters within the MSGT. The Hamilton principle is used to derive the equations of motion and the boundary conditions, and the Galerkin procedure is subsequently implemented to obtain the critical buckling load. Subsequently, the framework is extended to the thermally induced buckling behaviour, and three types of temperature rise patterns, namely uniform, linear and nonlinear temperature variations, along the thickness of the OSC are considered. Several verification studies are conducted to illustrate the accuracy of the present method. Besides, size-dependent material properties are taken into consideration during the numerical experiments. Thorough studies are conducted to demonstrate the difference between critical buckling loads obtained from the MSGT, the modified couple stress theory (MCST), and the classical plate theory (CPT) models. Furthermore, the effects of length scale parameter (h/l), the aspect ratio (a/b), the length-to-thickness ratio (a/h) and the Winkler-Pasternak elastic foundation parameters on the buckling behaviour of the OSC are also revealed by the numerical results.

Free vibration analysis of annular sector sandwich plates with FG-CNT reinforced composite face-sheets based on the Carrera’s Unified Formulation

This paper presents an investigation of the free vibration of annular sector sandwich plates with carbon nanotube reinforced face-sheets and various edges boundary conditions. It is assumed that carbon nanotubes are radially aligned and distributed uniformly (UD) or functionally graded (FG) in the thickness direction. The effective material properties of CNT reinforced face-sheets are estimated using the extended rule of mixture, which contains efficiency parameters to consider the size-dependent material properties. A variable kinematic model which has been utilized for FGM cases is extended to FG-CNTs to describe the continuous variation of properties through the thickness. In this paper, the Carrera’s Unified Formulation (CUF) is developed for the analysis of asymmetric sector plates for the first time. The governing equations and associated boundary conditions are obtained employing the Principle of Virtual Displacements (PVDs) based on the CUF and solved using the generalized differential quadrature (GDQ) method. Numerical results for some special cases are presented and validated by comparison with available results in the literature. Some numerical results are tabulated to show the effects of the volume fraction of carbon nanotubes, boundary conditions and geometrical parameters on the free vibration behavior of the annular sector sandwich structures with CNTRC face-sheets.

Vibration Analysis of Material Size-Dependent CNTs Using Energy Equivalent Model

This study presents a modified continuum model to investigate the vibration behavior of single and multi-carbon nanotubes (CNTs). Two parameters are exploited to consider size dependence; one derived from the energy equivalent model and the other from the modified couple stress theory. The energy equivalent model, derived from the basis of molecular mechanics, is exploited to describe size-dependent material properties such as Young and shear moduli for both zigzag and armchair CNT structures. A modified couple stress theory is proposed to capture the microstructure size effect by assisting material length scale. A modified kinematic Timoshenko nano-beam including shear deformation and rotary inertia effects is developed. The analytical solution is shown and verified with previously published works. Moreover, parametric studies are performed to illustrate the influence of the length scale parameter, translation indices of the chiral vector, and orientation of CNTs on the vibration behaviors. The effect of the number of tube layers on the fundamental frequency of CNTs is also presented. These findings are helpful in mechanical design of high-precision measurement nano-devices manufactured from CNTs.

Strong size-dependent stress relaxation in electrospun polymer nanofibers

Electrospun polymer nanofibers have garnered significant interest due to their strong size-dependent material properties, such as tensile moduli, strength, toughness, and glass transition temperatures. These properties are closely correlated with polymer chain dynamics. In most applications, polymers usually exhibit viscoelastic behaviors such as stress relaxation and creep, which are also determined by the motion of polymer chains. However, the size-dependent viscoelasticity has not been studied previously in polymer nanofibers. Here, we report the first experimental evidence of significant size-dependent stress relaxation in electrospun Nylon-11 nanofibers as well as size-dependent viscosity of the confined amorphous regions. In conjunction with the dramatically increasing stiffness of nano-scaled fibers, this strong relaxation enables size-tunable properties which break the traditional damping-stiffness tradeoff, qualifying electrospun nanofibers as a promising set of size-tunable materials with an unusual and highly desirable combination of simultaneously high stiffness and large mechanical energy dissipation.

A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment

In this paper, a new size-dependent plate model is developed based on the higher-order nonlocal strain gradient theory. The influences of higher-order deformations in conjunction with the higher- and lower-order nonlocal effects are taken into account. The presence of three different kinds of scale parameters in the formulation results in a theory which is capable of capturing both reduction and increase in the stiffness of structures at nanoscale. The governing differential equations are derived for the buckling of nanoplates resting on a two-parameter elastic foundation using the principle of virtual work. The nanoplate is assumed to be orthotropic with size-dependent material properties. The influence of thermal stress caused by a temperature change is taken into consideration. An exact closed-form solution is obtained for the critical buckling loads of graphene sheets. The higher-order governing differential equation is also solved by the differential quadrature method. The results of the two solution methods are compared with each other. Excellent agreement between the exact and numerical results is observed. For numerical results, three types of graphene sheets with different aspect ratio are considered. The effects of various scale parameters together with the other parameters such as the coefficients of the elastic medium, temperature change and the length of the nanoplate on the buckling behavior of graphene sheets are investigated.

In-situ Observation of Cross-Sectional Microstructural Changes and Stress Distributions in Fracturing TiN Thin Film during Nanoindentation.

Load-displacement curves measured during indentation experiments on thin films depend on non-homogeneous intrinsic film microstructure and residual stress gradients as well as on their changes during indenter penetration into the material. To date, microstructural changes and local stress concentrations resulting in plastic deformation and fracture were quantified exclusively using numerical models which suffer from poor knowledge of size dependent material properties and the unknown intrinsic gradients. Here, we report the first in-situ characterization of microstructural changes and multi-axial stress distributions in a wedge-indented 9 μm thick nanocrystalline TiN film volume performed using synchrotron cross-sectional X-ray nanodiffraction. During the indentation, needle-like TiN crystallites are tilted up to 15 degrees away from the indenter axis in the imprint area and strongly anisotropic diffraction peak broadening indicates strain variation within the X-ray nanoprobe caused by gradients of giant compressive stresses. The morphology of the multiaxial stress distributions with local concentrations up to −16.5 GPa correlate well with the observed fracture modes. The crack growth is influenced decisively by the film microstructure, especially by the micro- and nano-scopic interfaces. This novel experimental approach offers the capability to interpret indentation response and indenter imprint morphology of small graded nanostructured features.

Size- and temperature-dependent Young's modulus and size-dependent thermal expansion coefficient of thin films

Nanomaterials possess a high surface/volume ratio and surfaces play an essential role in size-dependent material properties. In the present study, nanometer-thick thin films were taken as an ideal system to investigate the surface-induced size- and temperature-dependent Young's modulus and size-dependent thermal expansion coefficient. The surface eigenstress model was further developed with the consideration of thermal expansion, leading to analytic formulas of size- and temperature-dependent Young's modulus, and size-dependent thermal expansion coefficient of thin films. Molecular dynamics (MD) simulations on face-centered cubic (fcc) Ag, Cu, and Ni(001) thin films were conducted at temperatures ranging from 300 K to 600 K. The MD simulation results are perfectly consistent with the theoretical predictions, thereby verifying the theoretical approach. The newly developed surface eigenstress model will be able to attack similar problems in other types of nanomaterials.

Serum protein adsorption and excretion pathways of metal nanoparticles.

While the synthesis of metal nanoparticles (NPs) with fascinating optical and electronic properties have progressed dramatically and their potential biomedical applications were also well demonstrated in the past decade, translation of metal NPs into the clinical practice still remains a challenge due to their severe accumulation in the body. Herein, we give a brief review on size-dependent material properties of metal NPs and their potential biomedical applications, followed by a summary of how structural parameters such as size, shape and charge influence their interactions with serum protein adsorption, cellular uptake and excretion pathways. Finally, the future challenges in minimizing serum protein adsorption and expediting clinical translation of metal NPs were also discussed.

Effects of eccentric circular perforation on thermal vibration of circular graphene sheets using translational addition theorem

In this article, nonlocal thin plate theory of Eringen is employed to investigate effects of thermal environment on behavior of freely vibrating circular single layer graphene sheet containing a circular perforation of arbitrary size and location. In order to analytically solve equation of motion, the separation of variables method in conjunction with the translational addition theorem for Bessel functions is used. Accuracy and stability of results are verified by the literature. The behavior of sheets in low and high temperature conditions is considered. The influences of temperature change and various geometrical parameters on the natural frequencies are investigated by considering size-dependent material properties. In some cases, thermal buckling phenomenon was observed. Results show that the temperature changes play an important role in free vibration behavior of eccentric circular graphene sheets.

Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment

In this paper, the axisymmetric buckling analysis of circular single-layered graphene sheets is studied by decoupling the basic constitutive equations based on the nonlocal theory of Eringen. The influences of temperature change, surface parameters and nonlocality on the buckling response of single-layered graphene sheet are investigated considering size-dependent material properties. Numerical solutions for buckling loads are computed using differential quadrature method (DQM). For comparison purpose, Galerkin method is also used to solve the nonlocal governing differential equation. DQM results are successfully verified with those of Galerkin method. The comparison of present results with the available molecular dynamics simulation data from the literature shows that the present formulation with appropriate values of surface and nonlocal parameters provides more accurate results than those obtained by the classical plate model. The results of present work can be used as benchmarks to evaluate future analyses of the circular nanoplates.

Static Behavior of FG-CNT Polymer Nano Composite Plate under Elevated Non-uniform Temperature Fields

In this paper, static behavior of functionally graded carbon nanotube reinforced polymer composite plate under non uniform elevated temperature fields has been investigated using finite element method. The effective material properties of the composite plate are obtained using the extended rule of mixture along with carbon nanotube efficiency parameters (to include size-dependent material properties). Parameter studies are carried out to analyze influence of boundary conditions of the plate, type of functional grading of the carbon nanotube and type of non uniform thermal loading on static behavior of the functionally graded carbon nanotube reinforced composite plate. It is found that static behavior of the composite plate has been significantly influenced by nature of temperature field and nature of functional grading of carbon nanotubes. Static bending deflection of the plate increases with volume fraction of the carbon nanotube except for unsymmetrical distribution of carbon nanotube.

Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

In this article, the nonlinear buckling characteristics of multi-layered graphene sheets are investigated. The graphene sheet is modeled as an orthotropic nanoplate with size-dependent material properties. The graphene film is subjected by non-uniformly distributed in-plane load through its thickness. To include the small scale and the geometrical nonlinearity effects, the governing differential equations are derived based on the nonlocal elasticity theory in conjunction with the von Karman geometrical model. Explicit expressions for the postbuckling loads of single- and double-layered graphene sheets with simply supported edges under biaxial compression are obtained. For numerical results, six types of armchair and zigzag graphene sheets with different aspect ratio are considered. The present formulation and method of solution are validated by comparing the results, in the limit cases, with those available in the open literature. Excellent agreement between the obtained and available results is observed. Finally, the effects of nonlocal parameter, buckling mode number, compression ratio and non-uniform parameter on the postbuckling behavior of multi-layered graphene sheets are studied.

Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model

Abstract This paper presents an investigation on the buckling and postbuckling of double-walled carbon nanotubes (CNTs) subjected to torsion in thermal environments. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Karman–Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent and are obtained from molecular dynamics (MD) simulations. The small scale parameter e 0 a is estimated by matching the buckling torque of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The results show that buckling torque and postbuckling behavior of CNTs are very sensitive to the small scale parameter e 0 a . The results reveal that the size-dependent and temperature-dependent material properties have a significant effect on the torsional buckling and postbuckling behavior of both single-walled and double-walled CNTs.

Loading History Effect on Size-Dependent Shear Strength of Pure and Nitrogen-Doped Ultrananocrystalline Diamond

A numerical study is performed to investigate the effect of loading history on the size-dependent material properties of pure and nitrogen-doped ultrananocrystalline diamond (UNCD) specimens under different shear loading paths. A simple procedure with combined kinetic Monte Carlo and molecular dynamics methods is adopted to form a polycrystalline UNCD with an artificial grain boundary (GB). By randomly adding different numbers of nitrogen atoms into the GBs, the effects of nitrogen doping and GB width on the UNCD responses under pre-compressioned/tensioned shear loading conditions are studied. It appears that the loading history has certain influence on the size-dependent material properties of UNCD, which provides useful information for formulating a multiscale constitutive model with applications to general cases.

Formation of GaSb core-shell nanofibers by a thermally induced phase decomposition process

Dense networks of amorphous GaSb nanofibers were fabricated by ion irradiation of bulk GaSb, and following formation, they were thermally annealed at a low temperature. Contrary to expectations, annealing of the GaSb fibers at just 50% of their melting temperature resulted in complete chemical decomposition of the nanofibers into core-shell structures consisting of crystalline Sb cores surrounded by amorphous shells. In this study, we investigate the transition of the single-phase nanofibers to their core-shell configuration, and we analyze the unique, temperature-dependent phase decomposition process. Thermodynamic considerations are discussed, and a model is presented to explain the thermally induced decomposition of the GaSb semiconductor fibers into core-shell structures, based upon the singular interaction of several size-dependent material properties.

The strength limit in a bio-inspired metallic nanocomposite

Large-scale molecular dynamics simulations are performed to investigate the plastic deformation behavior of a bio-inspired metallic nanocomposite which consists of hard nanosized Ni platelets embedded in a soft Al matrix. The investigation is restricted to an idealized nanocomposite structure with regular platelet distributions in a quasi-two-dimensional geometry under quasi-static loading conditions. This restriction enables us to study size dependent material properties over a wide range of length scales with a fully atomistic resolution of the material and thus without any a priori assumptions of the deformation processes. The simulation results are analyzed with respect to the prevailing deformation mechanisms and their influence on the mechanical properties of the nanocomposite with various geometrical variations. It is found that interfacial sliding contributes significantly to the plastic deformation despite a strong bonding across the interface. Critical for the strength of the nanocomposite is the geometric confinement of dislocation processes in the plastic phase, which strongly depends on the length scale and the morphology of the nanostructure. However, for the smallest structural scales, the softening caused by interfacial sliding prevails, giving rise to a maximum strength.