Contact Radius Research Articles

Design of low wear artificial hip joint considering 3D physiological loading and motion

Wear of the bearing surfaces of an artificial hip joint (AHJ) is one of the major causes to the premature failure of the prosthesis. Any design aiming at the surface wear reduction is of significance and the first primary understanding that should be achieved is to clarify the variation of the contact trajectories and the variation of the contact stresses and areas between the femoral head and acetabular cup of an AHJ while a person is walking or running.The purpose of present work is to develop an effective mechanism model to investigate the wear at the bearing surfaces of a hip joint prosthesis under the three-dimensional motion and loading conditions under patient’s walking activities. The femoral heads and acetabular cups of various dimensions were constructed by the finite element method to explore the effect of design parameters on the contact wear of their bearing surfaces. For an accurate prediction, the trajectory of the contact area in the bearing surfaces was analyzed, showing the variations in contact radius and contact stress. It was found that the sliding trajectory on the acetabular cup mainly concentrated in some specific regions. After 106 cycles of gait walking, an AHJ with thicker cup thickness or smaller femoral head radius would have less volumetric wear, whereas that with thinner cup thickness or larger femoral head radius would have less linear wear.

Multi-scale indentation model of stiff film-compliant substrate structures

As critical components or platforms, stiff film-compliant substrate structures are widely used in micro-electro-mechanical systems (MEMS) and other devices, in which their indentation behavior plays an important role. In this work, a multi-scale indentation model (MSI) for stiff film-compliant substrate structures is established based on the strain gradient theory and the surface elastic model. With this model, the indentation size effect of the structure is investigated from three aspects: the load-depth relationship, the distribution of bending moments in the film, and the surface morphology. The results show that the indentation size effect is mainly caused by the characteristic length and the surface residual stress of the film, and it is sensitive to the modulus ratio of the film to the substrate but has little relation with Poisson's ratio and the contact radius. Based on the above analysis, two dimensionless numbers are proposed to evaluate the indentation size effect of stiff film-compliant substrate structures. Besides, the predicted bending stiffness by the theoretical model is consistent with the experimental result, which verifies the effectiveness of the MSI model. Our research sheds light on the understanding of the indentation size effect of stiff film-compliant substrate structures and provides theoretical guidance for the design of related devices.

Axisymmetric Indentations of an Elastic Half-Space With Tensed Surface/Membrane in the Johnson–Kendall–Roberts Adhesive Approximation

Abstract Owing to the significant effects of adhesive force and surface/membrane tension, the classical contact models often fail to describe the indentation responses of soft materials and biological systems. This work addresses the axisymmetric indentation of an elastic substrate with constant surface/membrane tension by a spherical, conical, or cylindrical flat indenter in the Johnson–Kendall–Roberts adhesive approximation. On the basis of non-adhesive contact solutions accounting for the surface/membrane tension effect, explicit expressions for the external load and depth with respect to the contact radius are derived for the adhesive contact cases, which act as the theoretical fundamental for the accurate analysis of indentation tests. Despite using different correction functions, the results for spherical indentation are consistent with the solution of previous studies. It is found that the role of surface/membrane tension in the adhesive contact behavior is controlled by a dimensionless parameter. As the parameter gets larger, the pull-off force and the contact size at zero-external load for spherical and conical indentations are smaller, whereas the pull-off force for cylindrical flat indentation is higher.

Droplet evaporation on pillar structured surface: A 3D lattice Boltzmann numerical study

In this paper, a three-dimensional symmetric lattice Boltzmann (LB) model is built up to investigate evaporation of a sessile droplet on pillar structured surfaces. Parametric effects on droplet evaporation, including pillar structure size, roughness, temperature and wettability, are studied comprehensively, with emphasis on the variations of contact angle, contact radius and velocity of triple-phase contact line (TPCL) as well as heat and mass fluxes during evaporation. Pillar structures are found to induce the droplet to split into spherical cap part and liquid film part, resulting in an evaporation mode different from that on a plain surface. The extent of pinning-depinning is strongly associated with structures when TPCL retracts between pillars. Increasing surface temperature can accelerate evaporation by breaking the constant contact angle (CCA) mode, and increasing surface roughness accelerates evaporation by decreasing the duration of CCA mode. The majority of heat and mass transfer takes place around TPCL. High wettability can facilitate the evaporation of spherical cap due to the meniscus at liquid–vapor interface in the vicinity of pillar top surface. The substrate heat flux directly affected by structure size is higher in the region where pillars are distributed, and the solid–liquid interfacial heat flux varies with the specific interface location within droplet. The total mass flux primarily depends on the TPCL length determined by the droplet evaporation mode. When the droplet evaporates by partial penetration in the Cassie state, the amount of evaporation at liquid–vapor interface between pillars is greater than that above pillars. This paper provides more details and insights for a deep understanding of droplet evaporation on pillar structured surfaces.

Droplet evaporation dynamics on heterogeneous surfaces: Numerical modeling of the stick-slip motion

The interplay between the solid surface properties and transport phenomena during sessile droplet evaporation is extremely important in solid deposition processes. Engineering design requires realistic modeling of evaporation dynamics, on heterogeneous surfaces, which is very challenging. In this study, a continuum level, sharp-interface, ALE (Arbitrary Lagrangian- Eulerian) numerical model is developed. The model can efficiently deal with the problem of the moving three-phase contact line (TPL) during evaporation by incorporating the solid-liquid interactions in a Derjaguin pressure (commonly called disjoining pressure) term. It is found that, depending on the surface roughness and the material wettability, the evaporation dynamics proceeds following the Constant Contact Angle (CCA), Constant Contact Radius (CCR) or a mixed mode (stick-slip behavior). Numerical predictions concerning droplets evaporating on rough, hydrophobic substrates, are experimentally validated showing exceptional agreement. The stick-slip motion is found to appear during evaporation and is particularly affected by specific roughness features of the surface. Our findings are compared to Shanahan's theory. Interesting insights into the mechanisms of the stick-slip motion are presented for a rough hydrophobic substrate with weak pinning effects.

Evaporation of heated droplets at different wetting modes: A decoupled study of diffusive and convective effects

The evaporation of water droplets on the heated substrate exhibits diverse wetting modes such as Constant Contact Angle (CCA) mode, Constant Contact Radius (CCR) mode, and mixed mode. Coupled with multiple driving forces of vapor mass transfer, these wetting modes, especially mixed mode, have complex but unclear effects on droplet evaporation. The present study uses moving-mesh numerical simulation based on Arbitrary Lagrangian-Eulerian method to realize the evaporation of droplets at different wetting modes, and the simulation results of mixed mode evaporation agree well with experiments. The variations of temperature field during droplet evaporation are investigated, and the resemblance among diverse wetting modes can be attributed to the shape and the fluid flow intensity of the droplet. Decoupled analyses are conducted on the two major driving forces of evaporation for heated droplets at different wetting modes: diffusion and convection, and the effect of internal and external flows on the distribution of multiple mass fluxes along the droplet surface is elucidated. During droplet evaporation, CCR mode is more dependent on the diffusive effect, CCA mode is more dependent on the convective effect, and mixed mode lies in between. The present study elucidates the effect of wetting modes on the variation of multiple physical fields for the evaporation of heated droplets, promising in industrial and technological fields such as thermal management, droplet microfluidics, and medical treatment.

An Improved Static Membrane Deflection Analysis for Collapse Mode CMUT Fabricated by Sacrificial Release Method

To improve the accuracy of the static membrane deflection calculation for the collapse mode capacitive micromachined ultrasonic transducer (CMUT) fabricated by sacrificial release (SR) method. The beam theory was used and the substrate supporting force can be modeled by a coefficient to the load on the membrane. The surrounding supporting post bending can be modeled by applying the elastic support boundary conditions (ESBCs) for the peripheral part of the membrane. CMUT devices have been fabricated using the SR process to validate this analytical analysis. Young’s modulus of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {Si}_{{3}} \text {N}_{{4}}$ </tex-math></inline-formula> was derived as 200 GPa by a method using center deflections of several different radii single-layer conventional devices under 1 atm. The analytical deflection results and contact radius results for the collapse mode CMUT membranes were testified by experimental results under 1 atm and were found matching the experimental results. This showed that the analysis can provide improved results for SR fabricated CMUT devices by including the substrate supporting effect and the post bending effect.

Stress analysis and risk of failure during clenching in ceramic assembly models: 3-dimensional finite element analysis

Background/purposeClenching is a dental parafunctional disorder that jeopardizes the life of teeth and/or dental prostheses. Computer-aided design and computer-aided manufacturing (CAD/CAM)–fabricated or 3-dimensional-printed dental prostheses are aesthetic, strong, and of good quality, but noticeable damage can still be observed after clenching. Stress analysis of synthetic ceramic assemblies with various parameters was conducted to provide data that may be used to improve the fabrication of CAD/CAM–fabricated dental prostheses. Materials and methodsAbaqus software was used to run the simulations. A total of 96 axisymmetric finite element ceramic assembly models were simulated under 800 N vertical loading and different contact radii (0.25, 0.5, 0.75, 1.0 mm), materials (IPS e.max CAD and Vita Enamic), layer thicknesses and combinations. ResultsFour-layered ceramic assembly models produced promising results with the following parameters: contact radius of at least 0.5 mm, total thickness of at least 0.5 mm, and use of IPS e.max CAD as the first layer and Vita Enamic as the second layer without cement. ConclusionThe ideal four-layered assembly model design uses 0.25-mm-thick IPS e.max CAD as its outer layer to simulate enamel binding and 0.25-mm-thick Vita Enamic as its inner layer to imitate the natural tooth. This design may be used as reference for prosthodontic treatment.

Geometric optimization of pillars for enhanced adhesion

Interfaces with enhanced dry adhesion have applications in various fields, including robotic grasping and microtransfer printing. Arrays of pillars or fibers with mushroom-like geometries and variations on these have been used to achieve relatively strong adhesion to a broad range of surfaces via surface forces. Here, we investigate the optimal geometries for adhesive pillars through a gradient-based optimization scheme. The scheme minimizes an objective function based on the strain energy release rate of a crack at the pillar edge. The optimal design yields a stress distribution at the interface that is nearly-uniform and free from edge stress singularities. Experiments were performed on millimeter-scale pillars to evaluate the efficacy of the designs. A maximum adhesion enhancement of 2x was achieved for a pillar with a stalk radius equal to half of the contact radius. The location of crack initiation was shifted to the center of the pillar from the edge, indicating that the optimal design does indeed significantly reduce the stress concentration in the near-edge region. This geometric optimization scheme is versatile and can be extended to other scenarios where the control of stresses through geometry can be used to improve the performance of adhered interfaces and bonded joints.

Evaporation-induced self-assembly of gold nanorods on a hydrophobic substrate for surface enhanced Raman spectroscopy applications

The controllable assembly of plasmonic nanoparticles has developed as one of the most significant approaches for surface enhanced Raman spectroscopy (SERS) applications. This study developed a simple approach to improve a large-scale ordered assembly of gold nanorods (GNRs) by controlling the droplet evaporation mode on hydrophobic substrates. The hydrophobic substrate was efficiently produced by spin coating the silicone oil onto the glass slides and annealing them. The analyte molecule rhodamine (R6G) was employed as a surface-enhanced Raman scattering probe to demonstrate the potential effects of the synthesized arrays. This hydrophobic platform enables the concentration and delivery of analyte molecules into the surface enhanced Raman spectroscopy sensitive site while suppressing the coffee ring effect generated by the smooth contraction motion of the base contact radius of the droplet without any pinning. Thus, the limit of detection (LOD) of the R6G analyte was lowered to 10−10 M and the homogenous dispersion of surface enhanced Raman spectroscopy hotspots within the self-assembly reproducible surface enhanced Raman spectroscopy signal. This new method enables a broad range of packing patterns and mechanisms by changing the host nanoparticles in the dispersion.

Dynamics of intermetallics formation in the Al/Ni reactive wetting system

Due to the complexity of interfacial reactions during reactive wetting process at high temperatures, the intrinsic mechanism behind the formation and growth of intermetallic compounds (IMCs) is still unclear. This study presents insight into the possible formation of Al/Ni IMCs in the Al (l)/Ni (s) wetting system at 1023.15 K using molecular dynamics (MD) simulation. The reactive wetting process has been broadly classified into three regimes based on the Al/Ni interphase condition: fast spreading (mostly non-reactive), crossover (dissolutive), and slow-spreading (reactive). It is found that the intermetallic phases are nucleated during the dissolutive phase; however, the stable IMCs are formed during the reactive stage and are mostly composed of AlNi and Al3Ni5. The growth of IMCs in the radial direction shows the same behavior as the contact radius of the droplet, which is a significant increase of both the droplet radius and IMCs growth in the radial direction before the droplet reaches its quasi-equilibrium base radius. Quasi-equilibrium droplet radius occurs when changes in droplet radius are negligible. In a quasi-equilibrium regime, no significant change in droplet radius and IMCs growth is observed. In contrast, the IMCs growth in the normal direction shows the opposite behavior: the thickness of IMCs increases significantly during the quasi-equilibrium regime.

AMBER Free Energy Tools: A New Framework for the Design of Optimized Alchemical Transformation Pathways.

We develop a framework for the design of optimized alchemical transformation pathways in free energy simulations using nonlinear mixing and a new functional form for so-called "softcore" potentials. We describe the implementation and testing of this framework in the GPU-accelerated AMBER software suite. The new optimized alchemical transformation pathways integrate a number of important features, including (1) the use of smoothstep functions to stabilize behavior near the transformation end points, (2) consistent power scaling of Coulomb and Lennard-Jones (LJ) interactions with unitless control parameters to maintain balance of electrostatic attractions and exchange repulsions, (3) pairwise form based on the LJ contact radius for the effective interaction distance with separation-shifted scaling, and (4) rigorous smoothing of the potential at the nonbonded cutoff boundary. The new softcore potential form is combined with smoothly transforming nonlinear λ weights for mixing specific potential energy terms, along with flexible λ-scheduling features, to enable robust and stable alchemical transformation pathways. The resulting pathways are demonstrated and tested, and shown to be superior to the traditional methods in terms of numerical stability and minimal variance of the free energy estimates for all cases considered. The framework presented here can be used to design new alchemical enhanced sampling methods, and leveraged in robust free energy workflows for large ligand data sets.

Surfactant Control of Coffee Ring Formation in Carbon Nanotube Suspensions.

The coffee ring effect regularly occurs during the evaporation of colloidal droplets and is often undesirable. Here we show that adding a specific concentration of a surfactant can mitigate this effect. We have conducted experiments on aqueous suspensions of carbon nanotubes that were prepared with cationic surfactant dodecyltrimethylammonium bromide added at 0.2, 0.5, 1, 2, 5, and 10 times the critical micelle concentration. Colloidal droplets were deposited on candidate substrates for printed electronics with varying wetting characteristics: glass, polyethylene terephthalate, fluoroethylene propylene copolymer, and polydimethylsiloxane. Following drying, four pattern types were observed in the final deposits: dot-like, uniform, coffee ring deposits, and combined patterns (coffee ring with a dot-like central deposit). Evaporation occurred predominantly in constant contact radius mode for most pattern types, except for some cases that led to uniform deposits in which early stage receding of the contact line occurred. Image analysis and profilometry yielded deposit thicknesses, allowing us to identify a coffee ring subfeature in all uniform deposits and to infer the percentage coverage in all cases. Importantly, a critical surfactant concentration was identified for the generation of highly uniform deposits across all substrates. This concentration resulted in visually uniform deposits consisting of a coffee ring subfeature with a densely packed center, generated from two distinct evaporative phases.

Evaporation in thin film region of water at ambient temperature under reduced pressure conditions: Flow and interface characteristics

In this paper, the flow and interface characteristics of the thin liquid film region near the contact line of water under reduced pressure conditions are experimentally observed by using a multilayer nanoparticle image velocimetry technique. The results demonstrate that the flow in this region is promoted by reducing the pressure. The average velocities in the top layer of this region are 57.99, 61.52, 65.20, 66.00, and 68.25 μm/s at the degree of reduced pressure of 10–50 kPa with an interval of 10 kPa. Reducing the pressure shortens the evaporation time and advances the depinning time in the constant contact radius mode. Entering the constant contact angle mode, the initial height of the film increases, the critical height is elevated, and the decrease rate of film thickness increases, which leads to the shortening of the overall evaporation time. This work provides insight into the microscopic transport mechanisms of coolant under reduced pressure conditions.

Towards modeling and restraining surface ripples during bonnet polishing based on frequency domain characteristic control

Extensive research has been conducted on Bonnet polishing for its ability to manufacture freeform surfaces with nano-scale precision. However, surface ripples are easy to introduce under regular motion, and the underlying principle to address this problem remains unclear. In this study, a novel methodology based on frequency domain characterization is proposed, connecting the spatial process parameters and frequency domain evaluation index directly. Bessel function and single pulse convolution are introduced for model establishment. Tool radius, tool tilt angle, and contact radius are correlated with surface ripple mitigation. Polishing parameters optimization case study was conducted and verified using self-designed polishing robot.

Triple-line dynamics of a soft colloid-laden drop on a hydrophobic surface.

Evaporation of fluid from a pinned drop placed on solid surface proceeds via constant contact radius (CCR) mode, with a continuous reduction in the contact angle. The reduction of contact angle leads to an imbalance of interfacial tensions at the three-phase contact line. When the unbalanced force is sufficiently strong, the drop slips from the pinned contact line and slides inward. Depinning of the drop alters the mode of evaporation to constant contact angle (CCA) mode till it repins onto the surface. The change in evaporation mode from CCR to CCA is usually achieved by tuning the pinning energy barrier by controlling the surface properties of the substrate. Here, we demonstrate that the evaporation mode can be controlled by solely tailoring the surface tension of the drop, which is achieved in microgel particle-laden sessile drops that show spontaneous adsorption of microgels to the air/water interface, leading to a decrease in the interfacial tension. We show that droplets containing a sufficient number of microgels evaporate predominantly in CCR mode even on a hydrophobic surface, and the contact line remains pinned throughout the evaporation of the drop. Interestingly, the contact line dynamics can be controlled by tuning the softness of the microgels and the particle concentration in the drops.

"NUMERICAL SIMULATION OF ELASTIC-PLASTIC CONTACT WITH ISOTROPIC HARDENING "

The contacts of mechanical components transmit loads that lead to subsurface stresses developing in the contacting bodies. In an efficient tribological design, these stresses are expected to remain under the yield strength of the softer contacting material. When this condition is not met, plastic flow occurs in the softer body. Under the assumption of isotropic hardening, the yield strength increases with the development of additional plastic strains. As plastic flow processes are dissipative and therefore path dependent, the elastic-plastic problem is unsolvable through analytical endeavours, but can be approached with a numerical algorithm capable of simulating the loading history. The Betti’s reciprocal theorem provides the theoretical framework for the application of superposition principle to elastic-plastic stresses and displacement. An algorithm consisting in three nested loops is assembled from the solutions of simpler problems: (1) the purely elastic rough contact problem, (2) the inclusion problem and (3) the problem of the plastic strain increment. The numerical simulations suggest that the residual stresses decrease the intensity of the total stresses, thus delaying additional plastic flow. With increasing load, the heart-shaped plastic strain volume advances toward the surface, enveloping a plastic core near the initial point of contact. Compared to the purely elastic case, the elastic-plastic pressure shows a flatter distribution, while the contact radius is increased.

An investigation of Hertzian contact in soft materials using photoelastic tomography

Hertzian contact of a rigid sphere and a highly deformable soft solid is investigated using integrated photoelasticity. The experiments are performed by pressing a styrene sphere of 15 mm diameter against a 44 × 44 × 47 mm3 cuboid made of 5% wt. gelatin, inside a circular polariscope, and with a range of forces. The emerging light rays are processed by considering that the retardation of each ray carries the cumulative effect of traversing the contact-induced axisymmetric stress field. Then, assuming Hertz's theory is valid, the retardation is analytically calculated for each ray and compared to the experimental one. Furthermore, a finite element model of the process introduces the effect of finite displacements and strains. Beyond the qualitative comparison of the retardation fields, the experimental, theoretical, and numerical results are quantitatively compared in terms of the maximum equivalent stress, surface displacement, and contact radius dimensions. A favorable agreement is found at lower force levels, where the assumptions of Hertz theory hold, whereas deviations are observed at higher force levels. A major discovery of this work is that, at the maximum equivalent stress location, all three components of principal stress can be determined experimentally and show satisfactory agreement with theoretical and numerical ones in our measurement range. This provides valuable insight into Hertzian contact problems since the maximum equivalent stress controls the initiation of plastic deformation or failure. The measured displacement and contact radii also reasonably agree with the theoretical and numerical ones. Finally, the limitations that arise due to the linearization of this problem are explored.

An Extended Hertz Model for Incompressible Mooney–Rivlin Half-Space Under Finite Spherical Indentation

In this paper, an extended Hertz model is proposed to predict the mechanical responses of the incompressible Mooney–Rivlin half-space under finite spherical indentation. The contact behaviors are systematically investigated through the axisymmetric finite element (FE) model using various constitutive parameter ratios. Based on the numerical results, the radius of contact zone is first derived by adopting the exact function of the indenter shape. A reliable prediction of contact force, for the incompressible neo-Hookean model, is then obtained by substituting newly modified contact radius into the original Hertz model. From this base, a correction factor, which characterizes the effect of constitutive parameter ratio, is introduced to predict the contact force, and the contact pressure distribution of the original Hertz’ formula is also extended for the incompressible Mooney–Rivlin half-space under spherical indentation up to the indenter radius. The extended Hertz model related to constitutive parameters is validated effectively through FE simulations and experimental indentation results under finite spherical indentation. On the contrary, when the indentation depth exceeds 10% of the indenter radius, the original Hertz model is unable to predict the strong effect of constitutive parameter ratio on the contact behaviors for the incompressible Mooney–Rivlin half-space.

The Effect of Adhesion on Indentation Behavior of Various Smart Materials

The nanoindentation technique plays a significant role in characterizing the mechanical properties of materials at nanoscale, where the adhesion effect becomes very prominent due to the high surface-to-volume ratio. For this paper, the classical adhesion theories were generalized to study the contact behaviors of various piezoelectric materials indented by conical punches with different electric properties. With the use of the Hankel integral transform, dual integral equations, and superposing principle, the closed-form solutions of the physical fields for the Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models were obtained, respectively. The contribution of the electrical energy to the energy release rate under the conducting punch was taken into consideration. The relationships between the contact radius, the indentation load, and the indentation depth were set up using the total energy method for the JKR model and the Griffith energy balance for the M-D model, respectively. Numerical results indicate that increasing the half cone angle of the conical punch enhances the adhesion effect, which can significantly affect the accuracy of the results of characterization in nanoindentation tests. It was found that the effect of electric potential on adhesion behaviors is sensitive to different material properties, which are not revealed in the existing studies of axisymmetric adhesive contact of piezoelectric materials and multiferroic composite materials. The load-displacement curves under conical punches with different half cone angles have very different slopes. These results indicate that the half cone angle has a prominent effect on the characterization of mechanical properties of piezoelectric solids in nanoindentation tests.