Hertz Model Research Articles

The Effect of Acetylsalicylic Acid (Asa) on the Mechanical Properties of Breast Cancer Epithelial Cells.

In most communities, the risk of developing breast cancer is increasing. By affecting the cyclooxygenase 1 and 2 (COX-1 and COX-2) enzymes and actin filaments, acetylsalicylic acid (Aspirin) has been shown to reduce the risk of breast cancer and prevent cell migration in both laboratory and clinical studies. The purpose of this study is to determine the mechanical properties of normal and cancerous breast tissue cells, as well as the short-term effect of aspirin on cancer cells. To this end, the mechanical properties and deformation of three cell types were investigated: healthy MCF-10 breast cells, MCF-7 breast cancer cells, and MCF-7 breast cancer cells treated with a 5 μM aspirin solution. Atomic Force Microscopy (AFM) was used to determine the mechanical properties of the cells. Cell deformation was analyzed in all groups, and Young's modulus was calculated using the Hertz model. According to the obtained data, cancer cells deformed at a rate half that of healthy cells. Nonetheless, when aspirin was used, cancer cells deformed similarly to healthy cells. Additionally, healthy cells' Young's modulus was calculated to be approximately three times that of cancer cells, which was placed closer to that of healthy cells by adding aspirin to Young's modulus. Cell strength appears to have increased due to aspirin's intervention on actin filaments and cytoskeletons, and the mechanical properties of breast cancer cells have become more similar to those of normal cells. The likelihood of cell migration and metastasis decreases as cell strength increases.

Implementation of real contact behaviour in the DEM modelling of triaxial tests on railway ballast

In the Discrete Element modelling of soils, the micromechanical behaviour at contacts has often been considered to have a minor influence on the macromechanical response, leaving basic theoretical models (e.g., Hertz) to describe the contact response in the normal direction. A realistic description of the contact response may be crucial especially when investigating small strain ranges. Recent experimental inter-particle loading tests on gravel suggest that the classic contact models fail to reproduce certain mechanical features, especially when roughness is significant. Here, some of these experimental observations, including a softer response than the Hertz model under loading in the normal direction, and plasticity on unloading, are implemented in a DEM model for the simulation of small strain tests on railway ballast. The influence of these features on small strain stiffness is highlighted. A micromechanical analysis is carried out to show how each of the contact-level features introduced affects the macroscopic response. • Classic contact models do not work well for rough surfaces. • Accounting for lower normal stiffness due to contact with asperities and plasticity. • True contact behaviour implemented in numerical DEM simulations of ballast. • Contact behaviour can explain small strain stiffness degradation.

Changes in Mechanical Properties of Vesicles by Mucin in Aqueous Solution

The mechanical properties of vesicles were investigated as they were prepared, according to the ratio of mucin to dipalmitoylphosphatidylcholine (DPPC), using an atomic force microscope (AFM). After the confirmation of the vesicle adsorption on a mica surface, an AFM-tip deflection, caused by the interaction between the tip and the vesicle, was measured. The deflection showed that the tip broke through into the vesicle twice. Each break meant a tip-penetration into the upper and lower portion of the vesicle. Only the first penetration allowed the Hertzian model available to estimate the vesicle mechanical moduli. Two moduli reduced as the ratio of mucin to DPPC increased to 0.5, but the moduli were little changed above the 0.5 ratio. These results seem to be a platform for the effect of the mucin on the plasma-membrane anchoring and cellular signaling.

Experimental Evaluation of Theoretical Impact Models for Seismic Pounding

ABSTRACT One of the identified consequences of the aftermath of strong quakes is that structural pounding may trigger substantial damage including the collapse of colliding structures. This situation is attributed to inadequate distance between the adjacent structures. In order to address this concern, various numerical and experimental studies were conducted simulating earthquake induced pounding using different models of impact force. In this study, shaking table tests were conducted to assess the impact of seismic pounding between steel frame structures under near-field and far-field earthquakes. Five theoretical pounding force models, namely: linear spring, linear viscoelastic, Hertz, non-linear viscoelastic and Hertzdamp models were employed to replicate the pounding force. Various components of the theoretical models such as contact element stiffness, coefficient of restitution and impact damping ratio were calculated using the experimental results. Comparing the results of the Experimental Impact force time history with the prediction outcomes showed that the models over-predicted the pounding response. However, the prediction outcomes were congruent with the experimental results. Lastly, the linear viscoelastic model generated the least variance and most accurate predicted results compared to the other models. Hence, it can be inferred from the data that among other models, linear viscoelastic is the most accurate model to be used for the testing of pounding response.

A direct method for the extension of FastSim under non-Hertzian contact conditions

In wheel-rail contact mechanics, there coexist different models characterised by their ability to reproduce the real phenomenon and the time associated with computing the solution. In simulation of the vehicle dynamics, the increase in the computational performance places researchers close to a horizon in which it is possible to implement the most realistic theories (Variational Theory or finite elements), although at present the use of these models is mainly limited to offline calculations, far from real-time simulation. In this context, this work presents a tangential contact theory that is an intermediate point between simplified models (unable to model non-Hertzian contact) and more realistic models (whose complexity triggers simulation times). The tangential contact model proposed is based on the FastSim algorithm, whose precision comes from the algorithm convergence to the results of an exact adhesion theory (i.e. when creepages tend to zero). The impossibility of considering Kalker’s Linear Theory as an adjustment method when the hypotheses of the Hertzian model are not fulfilled leads to the adoption of the Kalker’s steady-state CONTACT version in adhesion conditions. The calculations presented through the proposed algorithm provide errors for creep forces lower than 4% with computational times one order lower than the Variational Theory.

P8. Responsiveness of patient derived intervertebral disc cells to mechanobiological treatment

P8. Responsiveness of patient derived intervertebral disc cells to mechanobiological treatment

Soft Contact Mechanics with Gradient-Stiffness Surfaces.

The stiffness in the top surface of many biological entities like cornea or articular cartilage, as well as chemically cross-linked synthetic hydrogels, can be significantly lower or more compliant than the bulk. When such a heterogeneous surface comes into contact, the contacting load is distributed differently from typical contact models. The mechanical response under indentation loading of a surface with a gradient of stiffness is a complex, integrated response that necessarily includes the heterogeneity. In this work, we identify empirical contact models between a rigid indenter and gradient elastic surfaces by numerically simulating quasi-static indentation. Three key case studies revealed the specific ways in which (I) continuous gradients, (II) laminate-layer gradients, and (III) alternating gradients generate new contact mechanics at the shallow-depth limit. Validation of the simulation-generated models was done by micro- and nanoindentation experiments on polyacrylamide samples synthesized to have a softer gradient surface layer. The field of stress and stretch in the subsurface as visualized from the simulations also reveals that the gradient layers become confined, which pushes the stretch fields closer to the surface and radially outward. Thus, contact areas are larger than expected, and average contact pressures are lower than predicted by the Hertz model. The overall findings of this work are new contact models and the mechanisms by which they change. These models allow a more accurate interpretation of the plethora of indentation data on surface gradient soft matter (biological and synthetic) as well as a better prediction of the force response to gradient soft surfaces. This work provides examples of how gradient hydrogel surfaces control the subsurface stress distribution and loading response.

Hertzian and adhesive plane models of contact of two inhomogeneous elastic bodies

Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterised by the Young modulus varying with depth as a power function. This paper models Hertzian and adhesive contact of two elastic inhomogeneous power-law graded bodies with different exponents. The problem is governed by an integral equation with two different power kernels. A nonstandard method of Gegenbauer orthogonal polynomials for its solution is proposed. It leads to an infinite system of linear algebraic equations of a special structure. The integral representations of the system coefficients are evaluated, and the properties of the system are studied. It is shown that if the exponents coincide, the infinite system admits a simple exact solution that corresponds to the case when the Young moduli are different but the exponents are the same. Formulas for the length of the contact zone, the pressure distribution and the surface normal displacements of the contacting bodies are obtained in the form convenient for computations. Effects of the mismatch in the Young moduli exponents are studied. A comparative analysis of the Hertzian and adhesive contact models clarifies the effects of the surface energy density on the contact pressure, the contact zone size and the profile of the contacting bodies outside the contact area.

Wind turbine main-bearing lubrication – Part 2: Simulation-based results for a double-row spherical roller main bearing in a 1.5 MW wind turbine

Abstract. This paper is the second in a two-part study on lubrication in wind turbine main bearings. Where Part 1 provided an introductory review of elastohydrodynamic lubrication theory, this paper will apply those ideas to investigate lubrication in the double-row spherical roller main bearing of a 1.5 MW wind turbine. Lubrication is investigated across a “contact conditions dataset” generated by inputting main-bearing applied loads, estimated from hub loads generated using aeroelastic simulation software, into a Hertzian contact model of the main bearing. From the Hertzian model is extracted values of roller load and contact patch dimensions, along with the time rate of change of contact patch dimensions. Also included in the dataset are additional environmental and operational variable values (e.g. wind speeds and shaft rotational speeds). A suitable formula for estimating film thickness within this particular bearing is then identified. Using lubricant properties of a commercially available wind turbine grease, specifically marketed for use in main bearings, an analysis of film thickness across the generated dataset is undertaken. The analysis includes consideration of effects relating to temperature, starvation, grease thickener interactions and possible non-steady effects. Results show that the studied main bearing is at risk of operating under mixed lubrication conditions for a non-negligible proportion of its operational life, indicating that further work is required to better understand lubrication in this context and implications for main-bearing damage and operational lifetimes. Key sensitivities and uncertainties within the analysis are discussed, along with recommendations for future work.

Mechanical characterization of multi-layered lipid nanoparticles using high-resolution AFM force spectroscopy

Lipid nanoparticles (LNPs) have been widely used in drug delivery systems. Their physicochemical properties play a substantial role in the pharmaceutical functions and therapeutic efficacy of encapsulated drugs. Although, numerous previous studies have examined the optimal physicochemical properties for drug delivery, the role of LNP mechanical compliance has not yet been established, owing to limitations imposed by their small size, extreme softness, and complex structures. The aim of this study was to delineate the true topography and the map of elastic moduli of LNPs by analyzing atomic force microscope (AFM) force spectroscopic data based on the modified Hertz model considering the asymptotic approach. Results reveal a hard core-soft shell structure of LNPs. Additionally, the elastic moduli of the core of LNPs are modulated from 176 kPa to 599 kPa through the addition of crosslinked alginate. However, a consistent elastic modulus (∼128 kPa) of outer shells is maintained regardless of core composition. In addition, Transwell assay show that, compared to rigid LNPs, those with soft properties exhibit enhanced permeation. This finding, which delineates the true topography and elastic moduli of LNPs, suggest an alternative for resolving the long-standing issues in AFM force spectroscopic studies.

Micromanipulation and Automatic Data Analysis to Determine the Mechanical Strength of Microparticles.

Microparticles are widely used in many industrial sectors. A micromanipulation technique has been widely used to quantify the mechanical properties of individual microparticles, which is crucial to the optimization of their functionality and performance in end-use applications. The principle of this technique is to compress single particles between two parallel surfaces, and the force versus displacement data are obtained simultaneously. Previously, analysis of the experimental data had to be done manually to calculate the rupture strength parameters of each individual particle, which is time-consuming. The aim of this study is to develop a software package that enables automatic analysis of the rupture strength parameters from the experimental data to enhance the capability of the micromanipulation technique. Three algorithms based on the combination of the “three-sigma rule”, a moving window, and the Hertz model were developed to locate the starting point where onset of compression occurs, and one algorithm based on the maximum deceleration was developed to identify the rupture point where a single particle is ruptured. Fifty microcapsules each with a liquid core and fifty porous polystyrene (PS) microspheres were tested in order to produce statistically representative results of each sample, and the experimental data were analysed using the developed software package. It is found that the results obtained from the combination of the “3σ + window” algorithm or the “3σ + window + Hertz” algorithm with the “maximum-deceleration” algorithm do not show any significant difference from the manual results. The data analysis time for each sample has been shortened from 2 to 3 h manually to within 20 min automatically.

Experimental and Numerical Analysis on the Impact Wear Behavior of TP316H Steel.

In this work, the contact force model and experiment methods were used to study the dynamic response and impact wear behavior of TP316H steel. The Flore model and the classic Hertz model were selected for comparison with the experimental results, and the model was revised according to the section parameters of the TP316H tube. The results show that there is a large difference between the models without considering the effect of structural stiffness on the impact system and the test results, whereas the revised model has a good agreement. With the rise in impact mass, the coefficient of restitution increases from 0.65 to 0.78, whereas the energy dissipation and wear volume decrease. Spalling, delamination, plastic deformation, and oxidative wear are the main impact wear mechanism of TP316H steel.

The Problem of Wedge Indenter with Flat-Rounded Bottom Indenting Half-Plane Elastic Body

In this paper, the problem of a wedge indenter with flat-rounded bottom indenting an infinite half-plane elastic body is solved. It can be used to study the penetration force or the surface stress distribution of the cutter when the tool intrudes into an elastic body. First, a first-order continuity method is proposed to eliminate the stress singularity caused by the sharp corners of the wedge indenter with flat bottom. The two-dimensional elastic contact problem is transformed into a Riemann–Hilbert boundary value problem with discontinuous coefficients expressed in the form of complex variables. For the frictionless contact problem, the explicit analytical solution is obtained for contact stress on the half-plane surface. Furthermore, the expression of the stress potential function is also derived to solve the stress field in the half-plane. Verification indicates that the wedge indenter with flat-rounded bottom can degenerate to several well-studied shaped indenters, including the Hertz model and flat-rounded model. The model in this paper is also validated with its numerical counterpart built in the finite element program LS-DYNA. Finally, the sensitivity of different configuration parameters on the normal contact stress and interior stress field in numerical model was investigated.

ПОДАТЛИВОСТЬ ПЛОСКОГО СТЫКА ФРАКТАЛЬНЫХ ПОВЕРХНОСТЕЙ

The work objective is to assess the compliance of a flat joint of fractal surfaces under load.
 The problem to which the paper is devoted is to assess the juxtaposition of fractal surfaces under load.
 Research methods: modeling of the contact interaction of the joint, analytical calculations.
 The novelty of the work: the bounds of applying models of contact interaction of surfaces (fractal and Hertz model) are defined and analyzed.
 Study results: the contact stiffness of flat surfaces joint for fractal models (plastic mode) and Hertz model (elastic mode) is defined, and the transfer point from one mode to another is found.
 Conclusions: with different roughness parameters, the joint compliance decreases with increasing load (increasing juxtaposition), and compliance under the same conditions increases with a decrease in roughness and an increase in fractal dimension D.

An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

SummaryAtomic force microscopy (AFM) is widely used for quantifying the mechanical properties of soft materials such as cells. AFM force-indentation curves are conventionally fitted with a Hertzian model to extract elastic properties. These properties solely are, however, insufficient to describe the mechanical properties of cells. Here, we expand the analysis capabilities to describe the viscoelastic behavior while using the same force-indentation curves. Our model gives an explicit relation of force and indentation and extracts physically meaningful mechanical parameters. We first validated the model on simulated force-indentation curves. Then, we applied the fitting model to the force-indentation curves of two hydrogels with different crosslinking mechanisms. Finally, we characterized HeLa cells in two cell cycle phases, interphase and mitosis, and showed that mitotic cells have a higher apparent elasticity and a lower apparent viscosity. Our study provides a simple method, which can be directly integrated into the standard AFM framework for extracting the viscoelastic properties of materials.

Investigating the effects of activation state and location on lower limb tissue stiffness

Lower limb tissue stiffness is contingent on various factors, including location, tissue composition, loading rates, and the geometry of the indenting object. Previous studies demonstrated that tissue stiffness varies greatly between individuals and between locations on an individual. Additionally, some studies have shown that activation of underlying muscle tissue increases bulk soft tissue stiffness. Yet, few studies have simultaneously considered both location and activation; this could be particularly important for measuring and predicting the function of devices such as prostheses and exoskeletons that interact with limbs at various locations during dynamic movement. In the present study, a custom handheld indentation device was used to explore changes in bulk leg tissue stiffness at rest and during isometric contractions. The indentation force-displacement curves were modelled using a Hertz model. At each level of activation (active/inactive), the shank had dramatically (∼150%) greater tissue stiffness than the thigh (p < 0.001). However, results suggested location independence for stiffness ratio (active/inactive, p = 0.42); for either location, stiffness was approximately 2x greater for active vs inactive muscle. These results should be considered during the development of biomechanical models to simulate human tissue indentation stiffness across a range of activation states and locations.

Influence of the Lander Size and Shape on the Ballistic Landing Motion

AbstractThis article investigates the ballistic landing motion and final distribution of the landers in different sizes or shapes near the small celestial body. Three typical shapes, including cubic, cuboid, and cylindrical, are considered for the landers deployed to a tri‐axial ellipsoid model. The Polygonal Contact Model (PCM) is used to detect the contact/collision, where the Hertz model is applied to calculate the continuous contact force. Different‐sized cubic landers (in the edge length of 20, 30, 40, and 50 cm) are numerically simulated to examine how the lander size influences its dynamics. The landing motion of the cuboid‐ and the cylinder‐shaped landers are then analyzed in the same technique. The heights of these asymmetrical landers are assumed to be 25, 30, and 35 cm, respectively, to illustrate the shape effect. Monte Carlo simulations are implemented for various landers to account for the surface motion randomness. The final dispersion, the outgoing velocity after the collision, the horizontal transfer distance, and the settling time are taken to be critical indicators for discussing the landing behavior, which can provide implications for the probe design of future missions.

Estimation of crack growth on rails under the combined influence of thermo-mechanical loading due to the sliding of wheel

Development and growth of surface and subsurface cracks on rail profile is one of the major reasons for deterioration of rails near the halting zones. Rail tracks are subjected to combination of thermal loads during the sliding motion of the wheel while braking and structural load due to the weight of the vehicle. In this paper, an FEA model is been developed to study and analyze the effect of coupled thermo-mechanical load during braking on contact stress and contact area at the rail-wheel interface. Both elastic and elasto-plastic FEA models are used and compared with analytical Hertzian approach to accurately predict rail-wheel contact parameters. A synthetic loading spectrum is proposed to simulate the combination of thermal and thermo-mechanical loading cycles on the rail during braking of vehicle. The loading cycle is used to predict the growth of previously present flaws using Modified Paris Law and Generalized Frost-Dugdale approach. It has been found that elasto-plastic FEA is inclined to predict lesser contact stresses than the elastic FEA or Hertzian model. Furthermore, shape of the contact patch for elasto-plastic FEA is observed to be unsymmetrical in the rolling direction unlike the elliptical contact area in elastic FEA approach. Macro scale initial cracks having length more than 2 mm are also realized to grow faster than their smaller counterparts under the combined effect of thermal and mechanical loads.

Comparative study of numerical simulation methods for seismic pounding of adjacent girder of curved girder bridges

Under seismic action, non-uniform collision will occur between the main beams of curved beam bridge, which may lead to local damage of front beam or rear beam. At present, the research on collision effect is mainly based on straight beam bridge, and there is still a lack of relevant research on seismic collision of curved beam bridge. Taking two adjacent typical curved bridges as examples, this paper establishes contact elements (linear elastic model, Kelvin model and Hertz model) and solid elements (three-dimensional contact friction model) which can fully reflect the physical characteristics of seismic collision of curved bridges. By comparing the numerical simulation methods of seismic collision, the advantages and disadvantages of the existing numerical simulation methods in the seismic response analysis of curved bridges are evaluated. The results show that the calculation results of Kelvin model and three-dimensional contact friction model have the least error and high calculation efficiency, and are suitable for the seismic analysis of curved beam bridges.

Orta Yükseklikteki Bitişik Nizam Yapılarda Çekiçleme Etkisinin İncelenmesi

Many adjacent structures have been built in recent years due to population growth and the unplanned urbanization. The mass and stiffness differences of the structures cause collions with each other. Since behavior of structures having different dynamic properties will be different, the pounding forces ocur between structures during earthquake. In this study, collision behavior in adjacent structures was investigated. The nonlinear spring Hertz model was used for modelling of collision. Existing structures were modeled with Sap 2000 program, by considering horizontal rigidity, story level and gap parameters as variables. Slab-column and slab-slab collision situations were taken into account in the structures. Dynamic analyses of the structures were performed by using Kocaeli earthquake data according to different gaps. Displacements and pounding forces of the structures were obtained and the results were compared. It was determined whether gaps calculated according to the Turkish Building Earthquake Code 2018 (TBEC-2018) were sufficient in the structures.