Modulus Gradient Research Articles

Adhesion Enhancement of Micropillar Array by Combining the Adhesive Design from Gecko and Tree Frog.

It has long been demonstrated the gecko-inspired micropillar array with T-shape tips possesses the best adhesion performance of a given material. The further enhancement of the adhesion performances of T-shape micropillars can offer redundant adhesion to compensate for the inevitable improper contacts. Here, the array of T-shape polydimethylsiloxane (PDMS) micropillars is incorporated with gradient dispersed calcium carbonate nanoparticles in the micropillar stalk, termed as T-shape gradient micropillars (TG), possessing the modulus gradient with stiff tip and soft root. The gradient modulus in TG facilitates the contact formation and regulates the stress at the detaching interface, resulting in a 4.6 times adhesion and 2.4 times friction as compared with the pure PDMS T-shape micropillar arrays. The study here provides a new design strategy for the super-strong structured dry adhesives.

Theoretical solution for the axial vibration of functionally graded double-lap adhesive joints

Adhesively bonded joints have widely been used in a number of engineering applications, owing to their improved mechanical performance as compared with other mechanical joining techniques, such as rivets or bolts. In this study, a theoretical solution of double-lap joints is established, with functionally graded adhesive and isotopic adherends, under harmonic loads. Assuming a parabolic distribution of the adhesive shear modulus along the overlap length, the analytical harmonic solution is expressed in terms of the solution of the nonlinear Heun differential equation. Furthermore, a two-dimensional finite-element model was developed to validate the analytical solution. We show that using softer adhesive at the edges of the bond line leads to less stress concentration. We also conclude that the adhesive’s shear modulus gradient along the bond line should be greater as the ratio of the adhesive’s shear stiffness to the adherends’ shear stiffness increases. An equation has also been established to determine the optimal shear modulus gradient in terms of the stiffness ratio.

Dynamical stability of embedded spinning axially graded micro and nanotubes conveying fluid

ABSTRACT In this study, the dynamical stability of spinning axially graded micro and nanotubes transporting fluid rested on the Kerr foundation is analyzed. A detailed parametric study is performed to clarify the effect of various factors such as axial material gradation and size-dependent parameters on the divergence and flutter instability thresholds of the system. To model the micro and nanofluidic systems, modified couple stress theory (MCST) and nonlocal strain gradient theory (NSGT) are implemented, respectively. The backward and forward vibrational frequencies, as well as critical divergence spin and fluid velocities of the system, are obtained. It is concluded that the stability evolution of spinning micro and nanostructures containing fluid can be altered by fine-adjustment of axial material gradation. Besides, it is found that the enhancement of elastic modulus gradient, strain gradient, material length scale, and foundation parameters improve the dynamical stability of the small-scale structures.

Surface instabilities in graded tubular tissues induced by volumetric growth

Growth-induced pattern formation in tubular tissues is intimately correlated to normal physiological functions. Moreover, either the microstructure or certain diseases can give rise to material inhomogeneity, which can lead to a change of shape in the tissue. Therefore, it is of fundamental importance to understand surface instabilities and pattern transitions of graded tubular tissues. In this paper we perform such analysis by the use of a mechanical model of a graded tube which grows with a fixed outer boundary by focusing on a plane-strain problem within the framework of nonlinear elasticity. A theoretical model is established to determine the uniform growth state, the critical growth factor, and the critical wavenumber for a general material model and for a general material gradient. For a case study, the material is specified by the neo-Hookean model, and the shear modulus is assumed to decay linearly or exponentially from the inner surface. Then, a parametric study is carried out to unravel the effects of material and geometrical parameters on the bifurcation threshold and the associated wrinkled pattern. In addition, a finite element model, which is validated by the theoretical one, is developed to trace the post-buckling evolution. It is found that wrinkled pattern will evolve into an arch mode and then into a creasing mode if the modulus decays linearly. However, the typical creasing mode may give way to a period-doubling mode when applying an exponentially decaying modulus, and there is a co-existence of the creasing mode and the wrinkling mode. As a result, different modulus gradients can generate diverse pattern formations. The obtained results are useful to supply insight into the effects of material inhomogeneity and different modulus gradients on surface instabilities and morphology evolutions in graded tubular tissues.

Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load

For the first time, the structural dynamics and vibrational stability of a viscoelastic axially functionally graded (AFG) beam with both spinning and axial motions subjected to an axial load are analyzed, with the aim to enhance the performance of bi-gyroscopic systems. A detailed parametric study is also performed to emphasize the influence of various key factors such as material distribution type, viscosity coefficient, and coupled rotation and axial translation on the dynamical characteristics of the system. The material properties of the system are assumed to vary linearly or exponentially in the longitudinal direction with viscoelastic effects. Adopting the Laplace transform and a Galerkin discretization scheme, the critical axial and spin velocities of the system are obtained. An analytical approach is applied to identify the instability thresholds. Stability maps are examined, and for the first time in this paper, it is demonstrated that the stability evolution of the system can be altered by fine-tuning of axial grading or viscosity of the material. The variation of density and elastic modulus gradient parameters are found to have opposite effects on the divergence and flutter boundaries of the system. Furthermore, the results indicate that the destabilizing effect of the axial compressive load can be significantly alleviated by the simultaneous determination of density and elastic modulus gradation in the axial direction of the system.

Establishment of multistage gradient modulus intermediate layer between fiber and matrix via designing double “rigid-flexible” structure to improve interfacial and mechanical properties of carbon fiber/resin composites

The gradient modulus intermediate layer between CF and epoxy by designing double “rigid-flexible” structure using CNTs and polyamide (PA) on the CF surface was firstly established, and the effects of modulus intermediate layer on interfacial and mechanical properties of CF composites were investigated. The constructing of double “rigid-flexible” structure on the CF surface can greatly increase the polar functional groups, roughness and wettability of the CF surface as well as the thickness of intermediate layer, which could balance the modulus of fiber and resin to achieve the best matching. The interfacial shear strength (IFSS), interlaminar shear strength (ILSS), flexural strength, and impact strength of CF composites increased by 75.6%, 44.1%, 41.3%, and 34.6%, respectively. In addition, the interfacial failure behaviors and strengthening mechanisms of composites have been studied. This novel design and method built a multistage gradient modulus intermediate layer of composite with strong physicochemical interaction and good wettability, which has greatly potential for high-performance composite.

3D printable tough silicone double networks

Additive manufacturing permits innovative soft device architectures with micron resolution. The processing requirements, however, restrict the available materials, and joining chemically dissimilar components remains a challenge. Here we report silicone double networks (SilDNs) that participate in orthogonal crosslinking mechanisms—photocurable thiol-ene reactions and condensation reactions—to exercise independent control over both the shape forming process (3D printing) and final mechanical properties. SilDNs simultaneously possess low elastic modulus (E100% < 700kPa) as well as large ultimate strains (dL/L0 up to ~ 400 %), toughnesses (U ~ 1.4 MJ·m−3), and strengths (σ ~ 1 MPa). Importantly, the latent condensation reaction permits cohesive bonding of printed objects to dissimilar substrates with modulus gradients that span more than seven orders of magnitude. We demonstrate soft devices relevant to a broad range of disciplines: models that simulate the geometries and mechanical properties of soft tissue systems and multimaterial assemblies for next generation wearable devices and robotics.

Vibration of spinning functionally graded nanotubes conveying fluid

As a first attempt, the vibration and stability analysis of magnetically embedded spinning axially functionally graded (AFG) nanotubes conveying fluid under axial loads is performed based on the nonlocal strain gradient theory (NSGT). A detailed parametric investigation is conducted to elucidate the influence of key factors such as material distribution type and size-dependent parameters on the divergence and flutter instability borders. Also, a comparative study is conducted to evaluate the available theories in the modeling of nanofluidic systems. The material characteristics of the system are graded along the longitudinal direction based on the power-law and exponential distribution functions. To accurate model and formulate the system, the no-slip boundary condition is considered. Adopting the Laplace transform and Galerkin discretization technique, the governing size-dependent dynamical equations of the system are solved. The backward and forward natural frequencies, as well as critical fluid and spin velocities of the system, are extracted. Besides, an analytical approach is applied to identify the instability thresholds of the system. Dynamical configurations, Campbell diagrams, and stability maps are analyzed. Meanwhile, it is concluded that, in contrast to the influence of nonlocal and density gradient parameters, the increment of strain gradient and elastic modulus gradient parameters expands the stability regions and alleviate the destabilizing effect of the axial compressive load.

Determination of complex modulus gradients of flexible pavements using falling weight deflectometer and artificial intelligence

The modulus gradient of asphalt concrete (AC) layers is an important feature of flexible pavements. The variation of the modulus with depth results from the synthetical effect of material properties, the service time of pavements, loading and environmental conditions. Since the modulus gradient directly affects critical responses and performance of pavements, the determination of the modulus gradient of AC layers is necessary for the evaluation, maintenance and rehabilitation of flexible pavements. This paper aims to propose a method to obtain layer moduli of flexible pavements at different loading frequencies, which include a power function describing the modulus gradient of AC layers. The method utilizes results from a typical nondestructive test in the field applying the falling weight deflectometer and techniques of the fast Fourier transform, finite element model updating, kriging model and artificial intelligence. The method is validated by comparing layer moduli obtained from the proposed method and other backcalculation softwares.

Functional significance of graded properties of insect cuticle supported by an evolutionary analysis.

The exoskeleton of nearly all insects consists of a flexible core and a stiff shell. The transition between these two is often characterized by a gradual change in the stiffness. However, the functional significance of this stiffness gradient is unknown. Here by combining finite-element analysis and multi-objective optimization, we simulated the mechanical response of about 3000 unique gradients of the elastic modulus to normal contacts. We showed that materials with exponential gradients of the elastic modulus could achieve an optimal balance between the load-bearing capacity and resilience. This is very similar to the elastic modulus gradient observed in insect cuticle and, therefore, suggests cuticle adaptations to applied mechanical stresses; this is likely to facilitate the function of insect cuticle as a protective barrier. Our results further indicate that the relative thickness of compositionally different regions in insect cuticle is similar to the optimal estimation. We expect our findings to inform the design of engineered materials with improved mechanical performance.

Numerical investigations on compressible non-linear fluid flow associated with a stress -sensitive fractured reservoir

ABSTRACT This paper emphasizes on the development of an improved mathematical model to understand the single-phase gas flow in a coupled matrix-fracture fluid mass exchange in a stress-sensitive reservoir along with the numerical investigations. Traditional methods for gas flow in fractured reservoirs don’t take into account the stress-sensitive fracture permeability. The focus of the present work is to study the highly nonlinear single-phase gas flow in a stress-sensitive fractured reservoir by using a dual-porosity model accompanied by the influence of quadratic gradient term in the fracture fluid flow equation. The results demonstrate that the stress-sensitivity of the fracture permeability negatively influences the pressure profiles and thus production. The pressure profile is underestimated when stress-sensitivity is not considered. The underestimation increases with increase in the pressure gradient and fracture permeability modulus. The underestimation is shown to vary from 106 Pa for constant pressure case to 105 Pa for constant rate case in the fracture. Additionally, higher fracture and matrix permeability results in an improved and homogeneous contribution throughout the rock-matrix. Thus, compared to the method used conventionally the present method can be employed to obtain more accurate pressure profiles and thus productivity of the reservoir.

Rebar corrosion monitoring using magnetic gradient and partial modulus

Abstract The rebar corrosion monitoring using magnetic method is a hot research area and it is necessary to develop effective methods using the rebar’s own magnetic characteristics with considerations of environmental magnetic field. In this paper, the magnetic gradient and partial modulus is proposed for rebar corrosion monitoring. The effectiveness of corrosion monitoring method is discussed on the basis of experimental results from eight rebars and four reinforced concrete beams before and after corrosion. The other three galvanized round steels are used to investigate the reliability and stability of the method. The results show that the percentage loss calculated by the magnetic gradient and partial modulus is basically consistent with the actual weight loss ratio and cross-sectional area loss ratio for uniform corrosion and the effects of environmental magnetic field can be negligible by using magnetic gradient and partial modulus, which shows promise for medium- and long-term monitoring in rebar corrosion.

Distribution of mechanical strain in equine distal metacarpal subchondral bone: A microCT-based finite element model

Microdamage accumulation and adaptation of subchondral bone subjected to intensive cyclic loading are important processes associated with catastrophic bone failure, and joint degeneration in athletic humans and racehorses. At the tissue-level, they lead to a spatial variation in bone tissue mineral density (TMD) which affects the response of the bone to mechanical load. Quantifying the spatial distribution of mechanical load within the subchondral bone is critical for understanding the mechanism of the joint failure. Previously, a gradient of TMD and mechanical properties has been reported under unconfined compression in osteochondral plugs. In the present study, we used micro computed tomography (μCT)-based finite element (FE) models of cartilage-bone to investigate the gradient of strain in the subchondral bone (SCB) from the third metacarpal (MC3) condyle of racehorses under simulated in situ compression. Non-destructive mechanical testing of specimens under high-rate compression provided the apparent-level modulus of SCB. FE models were analysed using unconfined and confined boundary conditions. Unconfined FE-predicted apparent-level gradient of modulus across the SCB thickness correlated well with the experimental results (R2 ​= ​0.72, p ​< ​0.05). The highest strain occurred in the most superficial SCB (0.5–2.5 ​mm deep to the cartilage-bone interface) under the simulated in-situ compression through articular cartilage. The findings of this study provide an estimation for the spatial distribution of mechanical strain within SCB in-situ in the presence of heterogeneous bone tissue which is commonly observed in joints subjected to intensive cyclic loading.

Gradient-induced droplet motion over soft solids

Abstract Fluid droplets can be induced to move over rigid or flexible surfaces under external or body forces. We describe the effect of variations in material properties of a flexible substrate as a mechanism for motion. In this paper, we consider a droplet placed on a substrate with either a stiffness or surface energy gradient and consider its potential for motion via coupling to elastic deformations of the substrate. In order to clarify the role of contact angles and to obtain a tractable model, we consider a 2D droplet. The gradients in substrate material properties give rise to asymmetric solid deformation and to unequal contact angles, thereby producing a force on the droplet. We then use a dynamic viscoelastic model to predict the resulting dynamics of droplets. Numerical results quantifying the effect of the gradients establish that it is more feasible to induce droplet motion with a gradient in surface energy. The results show that the magnitude of elastic modulus gradient needed to induce droplet motion exceeds experimentally feasible limits in the production of soft solids and is therefore unlikely as a passive mechanism for cell motion. In both cases, of surface energy or elastic modulus, the threshold to initiate motion is achieved at lower mean values of the material properties.

Stability of gravity-driven free-surface flow past a deformable solid: The role of depth-dependent modulus.

The linear stability of a Newtonian liquid layer flowing down an inclined plane lined with a deformable linear elastic solid characterized by a continuously varying modulus is analyzed in this study. A low-wave-number asymptotic analysis is performed to obtain an analytical expression for the complex wavespeed which shows striking similarity with the earlier results of Sahu and Shankar [Sahu and Shankar, Phys. Rev. E 94, 013111 (2016)10.1103/PhysRevE.94.013111] for gravity-driven flow of Newtonian fluid past a solid bilayer having constant shear modulus (in each layer) lined on a rigid inclined plane. This shows that a deformable solid layer having a continuously varying shear modulus can be treated as a generalization of a system having multiple solid layers of constant shear modulus. Also, in the low-wave-number limit, we show that the stability of the free surface is governed by the value of effective shear modulus G_{eff}, and not by the detailed spatial variation of the modulus. Here the effective shear modulus (H/G_{eff}=∫_{1}^{1+H}1/[E_{0}+E[over ¯](z)]dz, where [E_{0}+E[over ¯](z)] represents the modulus gradient function) characterizes the overall modulus of the elastic solid, which is obtained by treating the continuous variation to be the limit of the arrangement of solid layers of infinitesimal thickness (each having a constant shear modulus) in a series. At finite wave numbers, we show that the free-surface and the liquid-solid interface become unstable as we increase the value of Γ, where Γ indicates the ratio of viscous stresses in the fluid to elastic stresses in the solid. When the system is analysed for different types of spatial modulus variations, we find results similar to those of Gkanis and Kumar [Gkanis and Kumar, Phys. Rev. E 73, 026307 (2006)10.1103/PhysRevE.73.026307], i.e., when we have two different configurations of the shear modulus function that have the same spatially averaged modulus, but have different values at the interface, the system is more stable for the configuration having higher shear modulus at the liquid-solid interface. In a similar manner, when we examined systems having the same shear modulus at the liquid-solid interface and same average modulus, the more stable case is the one which has a higher value of shear modulus just below the interface. Thus the use of deformable solids with a depth-dependent modulus potentially offers more control in the passive manipulation of the instabilities.

Effects of ageing, temperature and frequency-dependent properties of asphalt concrete on top-down cracking

The horizontal tensile strain at the top of asphalt concrete (AC) layer is considered as the most appropriate response of pavement for analysing Top-down cracking (TDC). In this study, influence of vehicle speed, temperature and non-uniform aging modulus on TDC are explored according to tensile strain magnitudes at the pavement surface. Utilizing a new analysis approach, the responses are computed at top and bottom of thick and thin AC layers in pavements with cement-treated base (CTB) and granular base (GB). The results demonstrate that critical tensile strain arises at the top of AC layer and in transverse direction. Variations of speed at low temperature affect the critical type of cracking, while at intermediate and elevated temperatures TDC is dominant at all speeds analysed. It is shown that modulus gradient induced by aging is an influencing factor in TDC which causes critical location of TDC to vary at the surface significantly.

Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler–Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

Magneto-mechanical stability of axially functionally graded supported nanotubes

In this paper, size-dependent vibration analysis of axially functionally graded (AFG) supported nanotubes conveying nanoflow under longitudinal magnetic fields are performed, aiming at performance improvement of fluid-interaction nanosystems. Either the density or the elastic modulus of the AFG nanotube varies linearly or exponentially along the axial direction. Based on the nonlocal continuum theory, the higher-order dynamical equation of motion of the system is derived considering no-slip boundary condition. Galerkin discretization technique and eigenvalue analysis are implemented to solve the modeled equation. The validity of the simplified model is justified by comparing the results with findings currently available in the literature. Influence of material gradient, magnetic strength, and nonlocal parameter on the system’s stability is illustrated. The results indicated that the elastic modulus gradient parameter can profoundly displace the instability threshold of the system and the effect of the density profile is negligible. Stability analysis showed that by fine-tuning of material gradation, the nonlocal effect can be significantly alleviated. Furthermore, it was shown that at high or low values of elastic gradient parameters, the stability borders are highly sensitive to magnetic field strength. Results of this paper can be applied as a benchmark in the optimal design of nanofluidic systems.

Screw dislocation in a Bi-medium within strain gradient elasticity revisited

AbstractIn this paper, we consider a straight screw dis-location near a flat interface between two elastic media in the framework of strain gradient elasticity (as studied by Gutkin et. al. [1]) by now taking care of some incomplete calculations). Closed form solutions for stress components and the Peach-Koehler force on the dislocation have been derived. It is shown that the singularities of the stress components at the dislocation line are eliminated and both components are continuous and smooth across the interface. The effect of the distance of the dislocation position from the interface on the maximum value of stress is investigated. Unlike in the case of classical solution, the image force remains finite when the dislocation approaches the interface. It is shown that the dislocation is attracted by the medium with smaller shear modulus or smaller gradient coefficient.

Modulus distribution in polyacrylonitrile-based carbon fiber monofilaments

Modulus distribution in carbon fiber (CF) monofilament plays a key role in bridging the microscopic heterogeneous structures to the macroscopic mechanical properties, and is critical to understand its performance. Here, we present a quantitative measurement of the modulus distributions for a series of commercially available polyacrylonitrile (PAN)-based CFs (T300, T700S, T800H, T1000G and M40J from Toray) using plasma-assisted radius profiling method. The distribution, which is unique for each kind of CFs, shows a strong correlation to monofilament tensile properties. Based on the observations, we propose a mechanical model that reveals the dependence of the tensile strength of CF monofilament on the local modulus gradient and the local structural fluctuations. The work is a great improvement to the traditional skin-core model, and facilitates the design of high strength and high modulus CFs. The mechanical model can be generally applied to all kinds of fiber-shaped structures and materials.