A Theoretical Model for the Normal Contact Force of Two Elastoplastic Ellipsoidal Bodies

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Verena Becker ◽  
Marc Kamlah
Keyword(s):  
Theoretical Model ◽  
Contact Force ◽  
General Description ◽  
Element Analysis ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Static Contact ◽  
Elliptical Contact ◽  
Individual Grains ◽  
Force Displacement

Abstract To model the mechanical behavior of granular materials, a reliable description of the material properties is indispensable. Individual grains are usually not perfectly spherical. In batteries, for instance, lithium nickel manganese cobalt oxide (NMC) is a frequently used material, consisting out of particles with possibly ellipsoidal like shapes. As particles may plastically deform under increasing stresses, the paper presents a theoretical model for the normal contact force of elastoplastic ellipsoidal bodies for the use in the context of mechanical discrete element method (DEM). The model can be considered as extension of the elastic, elastic-plastic, fully plastic Thornton model by using a more general description to incorporate elliptical contact areas. The focus is on a normal contact force description as continuous function of time for all regimes, elastic, elastoplastic, and fully plastic loading, as well as unloading from elastoplastic loading, while the evolution of the plastic contact area is not considered here. All underlying formulae to describe the force-displacement relationship for the static contact problem are derived, partly based on finite element analysis (FEA). To verify the new model, FEAs are performed and their results compared with the model predictions.

A theoretical model for the contact of elastoplastic bodies

2001 ◽  
Vol 216 (4) ◽  
pp. 421-431 ◽  
Author(s):  
L-Y Li ◽  
C-Y Wu ◽  
C Thornton
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Contact Problems ◽  
Rigid Sphere ◽  
Element Analysis ◽  
Normal Contact ◽  
Perfectly Plastic ◽  
Static Contact ◽  
Elastic Perfectly Plastic ◽  
Force Displacement

The paper presents a theoretical model for the normal contact of a rigid sphere with an elastic-perfectly plastic half-space or an elastic-perfectly plastic sphere with a rigid wall. Formulae describing the force-displacement relationship for static contact problems and the coefficient of restitution for dynamic impact problems are derived. The present model can be considered as a modification of Johnson's model by using a more detailed pressure distribution function which is based on finite element analysis (PEA) results and considering the variation in the curvature of the contact surface during the contact interaction. In order to verify the theoretical model, finite element analyses are also conducted, and results are compared with those predicted by the model for both contact force-displacement relations and restitution coefficients. Good agreements between the model predictions and the FEA results are found.

Experimental Validation of a Volumetric Planetary Rover Wheel/Soil Interaction Model

2013 ◽  
Author(s):  
Willem Petersen ◽  
John McPhee
Keyword(s):  
Contact Force ◽  
Interaction Model ◽  
Contact Model ◽  
Soil Parameters ◽  
Model Parameters ◽  
Force Model ◽  
Normal Contact ◽  
Planetary Rover ◽  
Normal Contact Force ◽  
Contact Force Model

For the multibody simulation of planetary rover operations, a wheel-soil contact model is necessary to represent the forces and moments between the tire and the soft soil. A novel nonlinear contact modelling approach based on the properties of the hypervolume of interpenetration is validated in this paper. This normal contact force model is based on the Winkler foundation model with nonlinear spring properties. To fully define the proposed normal contact force model for this application, seven parameters are required. Besides the geometry parameters that can be easily measured, three soil parameters representing the hyperelastic and plastic properties of the soil have to be identified. Since it is very difficult to directly measure the latter set of soil parameters, they are identified by comparing computer simulations with experimental results of drawbar pull tests performed under different slip conditions on the Juno rover of the Canadian Space Agency (CSA). A multibody dynamics model of the Juno rover including the new wheel/soil interaction model was developed and simulated in MapleSim. To identify the wheel/soil contact model parameters, the cost function of the model residuals of the kinematic data is minimized. The volumetric contact model is then tested by using the identified contact model parameters in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain and compared against experiments.

Shape Optimal Design of Contact Springs of Electronic Connectors

2002 ◽  
Vol 124 (3) ◽  
pp. 178-183 ◽  
Author(s):  
Yeh-Liang Hsu ◽  
Yuan-Chan Hsu ◽  
Ming-Sho Hsu
Keyword(s):  
Contact Force ◽  
Printed Circuit Boards ◽  
Normal Force ◽  
Optimization Techniques ◽  
Contact Forces ◽  
Design Parameters ◽  
Original Design ◽  
Insertion Force ◽  
Element Analysis ◽  
Normal Contact

An electronic connector provides a separable interface between two subsystems of an electronic system. The contact spring is probably the most critical component in an electronic connector. Mechanically, the contact spring provides the contact normal force, which establishes the contact interface as the connector is mated. However, connector manufacturers have a basic struggle between the need for high normal contact forces and low insertion forces. Designing connectors with large numbers of pins that are used with today’s integrated circuits and printed circuit boards often results in an associated rise in connector insertion force. It is possible to lower the insertion force of a connector by redesigning the geometry of the contact spring, but this also means a decrease in contact normal force. In this paper, structural shape optimization techniques are used to find the optimal shape of the contact springs of an electronic connector. The process of the insertion of a PCB into the contact springs of a connector is modeled by finite element analysis. The maximum insertion force and the contact normal force are calculated. The effects of several design parameters are discussed. The geometry of the contact springs is then parameterized and optimized. The required insertion force is minimized while the normal contact force and the resulting stress are maintained within specified values. In our example, the insertion force of the final contact spring design is reduced to 68.3% of that of the original design, while the contact force and the maximum stress are maintained within specified values.

Normal and Angular Motions at Rough Planar Contacts During Sliding With Friction

1992 ◽  
Vol 114 (3) ◽  
pp. 567-578 ◽  
Author(s):  
D. P. Hess ◽  
A. Soom
Keyword(s):  
Nonlinear Equations ◽  
Contact Force ◽  
Contact Area ◽  
Normal Contact ◽  
Frictional Contacts ◽  
Normal Contact Force ◽  
The Real ◽  
Real Area Of Contact ◽  
Real Area ◽  
Contact Vibrations

The planar dynamics of a rough block in nominally stationary or sliding contact with a counter-surface is studied in this work. Starting with the Greenwood-Williamson model of a rough surface, the analysis of elastic contact deflections is extended to accommodate angular as well as normal motions. The real area of contact and the normal contact force are obtained in terms of the relative approach and orientation of the surfaces. It is shown that angular and normal motions at frictional contacts are generally coupled. The contact area and normal contact force are shown to be nonlinearly related to the normal and angular motions. However, the contact area remains proportional to the normal load, even in the presence of angular motions. When the friction force is assumed to be proportional to the real area of contact, the coefficient of sliding friction will be unchanged by small relative rotations between the sliding bodies. Based on this contact and friction model, the nonlinear equations of motion that describe the planar contact vibrations of a sliding block can be written directly. Although a detailed analysis of the stability and response characteristics of these nonlinear equations is beyond the scope of the present work, a limited comparison of calculations and measurements taken on both stationary and sliding blocks indicate that the small amplitude contact vibrations are reasonably well captured by the model developed in this work.

Elastic-Plastic Finite-Element Analysis of Repeated, Two-Dimensional Wheel-Rail Rolling Contact under Time-Dependent Load

2006 ◽  
Vol 220 (5) ◽  
pp. 603-613 ◽  
Author(s):  
Z. F. Wen ◽  
X. S. Jin
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Contact Force ◽  
Rolling Contact ◽  
Time Dependent ◽  
Two Dimensional ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Residual Strains ◽  
Harmonic Variation

A study was performed using a finite-element model to obtain stresses, strains, and deformations for repeated, two-dimensional rolling contact of a locomotive driving wheel and a rail under time-dependent load. An advanced cyclic plasticity model was used with a commercial finite element code via a material subroutine. The time-dependent load was considered a harmonic variation of the wheel-rail normal contact force. The normal contact pressure was assumed to follow the Hertzian distribution and the tangential force followed the Carter distribution. A wavy profile is formed on the running surface of the rail subjected to the harmonic variation of the normal (vertical) contact force. The developed wavelength of the profile corresponds to the frequency of the normal contact force for the actual train speed. The creepage or rolling-sliding condition plays an important role in the residual strains and deformations, but its influence on the residual stresses is insignificant. The residual stresses at the surface decrease with increasing rolling passes and gradually tend to stabilize. The residual strains and surface displacements increase with increasing rolling cycle, but the increases in residual strain and surface displacement per rolling pass (ratchetting rate) decay. The residual stresses, strains, and deformations near the wave trough of the residual wavy deformation are larger than those near the wave crest. For any given creepage including zero value, when the number of rolling passes increases, the surface depth of the wavy-deformed surface increases but the ratchetting rate decays. The results are useful in investigating the influence of plastic deformation on rail corrugation.

Research on Normal Motion of Specimen of Ultrasonic Feeding

2012 ◽  
Vol 433-440 ◽  
pp. 3826-3830
Author(s):  
Liang Li ◽  
Mian Zheng
Keyword(s):  
Contact Force ◽  
Structural Model ◽  
Contact Process ◽  
Low Frequency ◽  
Normal Velocity ◽  
Normal Contact ◽  
Nonlinear Dynamical ◽  
Normal Contact Force ◽  
Theoretical Results ◽  
Good Agreement

In this paper, a micro structural model is applied to study the normal contact process of the specimen of the ultrasonic feeding. Firstly, the normal velocity of the specimen with the actuation of the oscillator is calculated by solving the nonlinear dynamical equation of the specimen. The theoretical results of the normal velocity are in good agreement with the experimental results under the same conditions. The theoretical results indicate that for the low frequency of the oscillator, at most time, the normal contact force is zero, whereas for the high frequency the normal contact force is periodical. In addition, the theoretical results also indicate the contact time between specimen and the oscillator in a period decreases with the increasing amplitude of the oscillator.

scholarly journals An Electronic Force Sensor for Medical Jet Injection

2019 ◽  
Vol 13 (2) ◽  
Author(s):  
Nickolas P. Demas ◽  
Ian W. Hunter
Keyword(s):  
Contact Force ◽  
Mean Absolute Error ◽  
Force Sensor ◽  
Absolute Error ◽  
Jet Injection ◽  
Lateral Direction ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Force Magnitude ◽  
Lateral Contact

In medical jet injection, a narrow fluid drug stream is propelled at high velocity into skin without a needle. Previous studies have shown that the volume delivered is highly dependent on a number of factors. This paper details the development of an electronic force sensor for medical jet injection and shows that the normal contact force exerted on the tissue by the nozzle is an additional factor affecting volume delivered. Using this sensor, we measure the forces at the nozzle tip in the normal direction with a sensitivity of 18 μN, calibrated over a range from 1 N to 8 N with a mean absolute error of 8 mN, and a maximum overload of 300 N. We further measure forces at the nozzle tip in the lateral direction with a sensitivity of 8 μN, calibrated over a range from 0.1 N to 7 N, with a mean absolute error of 101 mN for lateral contact force magnitude and 1.60 deg for lateral contact force direction. Experimental validation confirms that the force sensor does not adversely affect the accuracy and precision of ejected volume from the jet injector. We use this setup to examine the effect of normal contact force on volume delivered into postmortem porcine tissue. Experimental results demonstrate that volume delivered with normal contact force between 4 N and 8 N is significantly more accurate and precise compared to volume delivered with normal contact force between 0 N and 3.9 N.

A normal contact force approach for viscoelastic spheres of the same material

2019 ◽  
Vol 350 ◽  
pp. 51-61 ◽  
Author(s):  
B. Jian ◽  
G.M. Hu ◽  
Z.Q. Fang ◽  
H.J. Zhou ◽  
R. Xia
Keyword(s):  
Contact Force ◽  
Normal Contact ◽  
Normal Contact Force

A Contact Model of Nominally Flat Rough Surfaces Based on a Visco-Elasto-Adhesive Interaction

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
W. Cheng ◽  
K. Farhang
Keyword(s):  
Closed Form ◽  
Contact Force ◽  
Rough Surfaces ◽  
Mathematical Formulation ◽  
Power Laws ◽  
Adhesive Interaction ◽  
Time Rate ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Rate Dependent

Approximate closed-form equations are derived for normal contact force between nominally flat rough surfaces in dry contact. The formulation is based on the asperity-level interaction in which adhesive forces between two asperities and elastic and rate-dependent forces are included. The elastic and time rate-dependent portion of force is derived using a viscoelastic interaction of the two asperities. Statistical consideration of rough surfaces then furnishes the mathematical formulation of total normal force due to adhesion, elastic, and rate-dependent properties of the solids in contact. The probabilistic formulation of contact force leads to integral equations. From these are derived approximate closed-form expressions that relate the microscale properties of the surfaces to the macroscale behavior in the form of the total normal contact force between the surfaces. The approximate equations for visco-elasto-adhesive contact of rough surfaces illustrate the dependence of the contact force on the time rate of approach based on a combination of 1/6, 1/3, and 1 power laws.

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