Elastic Force Model Research Articles

Atomistic simulations of distortion-limited high-speed dynamics of antiferromagnetic skyrmions

In antiferromagnetic (AFM) materials, localized self-sustaining states called solitons, namely, domain walls (DWs) and skyrmions, can be efficiently driven by currents and achieve velocities of several kilometers per second. These solitons are massive particles and therefore cannot travel faster than a limiting velocity akin to the speed of light for the material. The specifics of these high-velocity dynamics, in which solitons begin to display relativistic effects, have been well understood for the case of DWs (single-dimensional particles). Here, we perform an extensive and systematic atomistic study of both one-dimensional and two-dimensional soliton dynamics in chiral magnetic materials, both at and away from angular momentum compensation. We develop an elastic restorative force model to explain the dynamic skyrmion deformations, supported by simulation data. We claim that these deformations arise from a local imbalance of gyrotropic forces. We also present an outlook on the role of skyrmion compactness in their deformation patterns, velocity limits, as well as the absence of behaviors similar to ones observed in relativistic DWs. We claim that limits on skyrmion compactness also impede their ability to reach the velocity regime where relativistic effects begin to occur in rapidly moving DWs, due to the critical skyrmion breakdown behavior. These results could prove to be significant to the field of spintronics, as well as the potential applications of skyrmions for novel logic and memory devices.

Dual Vibration Reduction Structured Active Suspension via Bushing Spring and Corresponding Nonlinear Parameter Visual Optimization Based H2/H∞ Controller

A common bushing is suggested to be upgraded into a bushing spring by thickening the rubber layer to pragmatize the dual vibration reduction structured (DVRS) active suspension. To remedy negative influence of the actuator equivalent inertial mass on the vertical vibration performance of the active suspension utilizing the rotary-motor actuator, a DVRS active suspension scheme via bushing spring is proposed and its corresponding nonlinear controller is specially developed. The “quasi-saturation” damping force and “inverse S-shaped” elastic force model is proposed to match the bushing spring test data. The corresponding nonlinear parameter visual optimization based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller is specially developed to deal with the nonlinear factors of the DVRS active suspension and the absence of linear damping of the bushing spring. Simulation and hardware-in the-loop experimental results corroborate the effectiveness of the featured DVRS active suspension regulated by the specially designed controller with good performances under both D-class and bumpy road running conditions, especially in reducing the body acceleration and improving vehicle ride comfort.

Dynamics of stochastic vibro-impact oscillator with compliant contact force models

The focus of this study is on numerically investigating the effects of additive noise on the dynamics of vibro-impact oscillators with compliant supports. Various models for the compliant supports have been considered, which include elastic, elasto-plastic, linear and nonlinear dissipative contact force models, and which follow constitutive laws that are discontinuous. It has been shown that noise superimposed on the harmonic excitations alters the dynamical features of the non-smooth systems significantly. Stochastic bifurcation analyses have been carried out to investigate the stability characteristics of the systems with respect to the different compliant force models and a comparison has been presented on the advantages and limitations of the various contact force models in the presence of noisy excitations.

Effectiveness of Using Polymer Bumpers to Mitigate Earthquake-Induced Pounding between Buildings of Unequal Heights

Collisions often happen between adjacent buildings without a sufficient gap under seismic loadings. Installing polymer bumpers may decrease the pounding forces between colliding buildings. This paper focuses on the analysis of suppressing pounding effects by using of polymer bumpers. In order to investigate pounding mitigation effectiveness in the condition with and without bumpers, different types of pounding force models are utilized to simulate and calculate frame vibration responses under seismic loads. Firstly, time-history results for pounding force, displacements, and shearing forces in selected floors are calculated in the condition with and without polymer bumpers. Secondly, differences between viscoelastic and elastic pounding force models are compared and discussed. And finally, parametric studies are carried out to investigate influences of different pounding parameters. The results show that polymer bumpers can reduce maximum values of pounding force but increase pounding times. And viscoelasticity of bumper materials has a certain range of influences on pounding force responses. Choosing improper material types and pounding parameters may lead to opposite effects.

An arbitrary Lagrangian–Eulerian discretization method for modeling and simulation of reeving systems in multibody dynamics

This paper presents an efficient discretization method for the modeling and simulation of reeving systems using multibody dynamics. Reeving systems are assumed to include rigid bodies connected by a set of sheaves or reels and wire ropes. The method is based on line-parametrized Absolute Nodal Coordinate Formulation (ANCF) defined in the framework of an Arbitrary Lagrangian–Eulerian (ALE) description. In the ALE description the element nodes have variable material coordinates thus allowing the element to change its position within the flexible body. This property is very convenient to model wire ropes rolled in sheaves or reels that have variable-length free spans, as usually occurs in reeving systems. Axial-torsion elastic coupling of the wire ropes is also a very important effect to be considered in reeving systems. A set of locally defined cross-section rotation angles is introduced to describe this effect thus abandoning the ANCF formalism. This paper presents different options for the wire rope modeling depending on the problem dimension (1, 2 or 3D) and the assumed elastic force model. Depending on the application the method offers elements that can show axial, torsion and bending deformation energies or any combination of them. This paper presents a general procedure to model reeving systems and the numerical calculation of the resulting equations of motion. Two examples are presented: the dynamic model of a 2:1-suspended electrically-driven elevator and a quasi-static model of a large crane.

A continuous contact force model of planar revolute joint based on fitting method

Both the process of eliminating the clearance in joints and the contact–impact process involve movement of a clearance mechanism, which may reduce transmission accuracy and lengthen the response time. An appropriate continuous contact force model is able to describe the contact phenomena of a joint with clearance in a facile manner. However, two main problems still should be solved in building the continuous contact force model. First, the elastic force parts in previous continuous contact force models for a revolute joint were established by amending the force exponent of the Hertz spherical contact model or by the modified Winkler contact model. Nevertheless, the force exponent is usually given by experience, and the thickness of the elastic layer in the Winkler theory is difficult to determine. Second, for the previous damping force parts of a revolute joint, the hysteretic damping coefficients were obtained by substituting the stiffness coefficient with the contact stiffness of revolute joint directly instead of using the energy conservation method for the complicated form of elastic force model. A feasible continuous contact force model based on a fitting method was proposed to avoid these problems. According to the experimental results, the continuous contact force model can be used to predict the contact characteristics of a planar revolute joint in a facile manner.

Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation

With the development of space technology, flexible appendages such as lightweight manipulators and satellite antennas, often appear in spacecrafts. Usually, the large overall motion of the flexible appendage will bring about large deformation problem. And there is a strong nonlinear coupling between the large overall motion and deformation of the flexible appendage, which brings about a large challenge to the precise control of the spacecraft. Dynamics of a rotating flexible planar beam with large deformation is investigated in this paper. A new nonlinear dynamic model of a flexible beam with large deformation is established based on an absolute node coordinate formulation (ANCF). The longitudinal and bending deformations of the flexible beam are both considered in the model. The longitudinal strain energy and bending strain energy of the beam can be calculated by using Green-Lagrangian strain tensor and the exact expression of the flexible beam curvature, respectively. A new concise expression of the bending deformation energy can be obtained by using the Lagrange identical equation. The new elastic force model is derived from the new expression of the deformation energy. The dynamic equations of the present model can precisely deal with the large deformation problem of flexible beams. Then, simulation results from three dynamic models, including the ANCF model, the high order coupling model (HOC model), and the BEAM188 model in ANSYS, are compared to prove the validity of the ANCF model proposed in this paper. And we can also find the deficiency of the HOC model from the simulation. Further study shows that the new generalized elastic force model can be simplified properly. Two simplified models are presented in this paper. The applicabilities of the simplified models are pointed out from the viewpoints of computational efficiency and accuracy. A dimensionless parameter denoted as is introduced to describe the extent to which a flexible beam pendulum undergoing free falling motion is deformed. The deformation of the flexible beam increases as increases. Considering the calculating efficiency of the dynamic model, when is small, simplified model I is chosen preferentially; when is big, simplified model Ⅱ is adopted preferentially.

Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law

Non-linear constitutive models of the elastic forces for a hyperelastic material are presented. Three elastic force models including Neo-Hookean, Mooney-Riblin 2nd, and Yeoh models are derived based on non-linear continuum mechanics. Elastic forces are applied to the three-dimensional absolute nodal coordinate beam element, and the transient response of the cantilever beam is analyzed. Simulation results are compared to experiment data, and the dynamic characteristics of elastic force models presented in this paper are discussed.

Comparison Between Elastic Foundation and Contact Force Models in Wear Analysis of Planar Multibody System

In this paper, two procedures to analyze planar multibody systems experiencing wear at a revolute joint are compared. In both procedures, the revolute joint of interest includes a clearance whose shape and size are dictated by wear. The procedures consist of coupled iterative analyses between a dynamic system analysis with nonideal joints and a wear prediction to determine the evolution of the joint clearance. In the first procedure, joint forces and contact pressures are estimated using the elastic foundation model with hysteresis damping via the dynamic analysis. In the second procedure, a contact force model with hysteresis damping is used to estimate the joint forces. In the latter case, however, the contact pressure is estimated using a finite element method (FEM). A comparison in performance of the two models is facilitated through the use of an experimental slider-crank mechanism in which wear is permitted to occur at one of the joints. It is observed that the two procedures provide similar estimates for the dynamic response and wear volumes but substantially different predictions on the wear profiles. Additionally, experimental results show that while predictions on the wear volume from both models are reasonably accurate, the FEM-based model produced more accurate predictions on the wear profile.

Discrete element modeling of direct shear tests for a granular material

AbstractA succinct 3D discrete element model, with clumps to resemble the real shapes of granular materials, is developed. The quaternion method is introduced to transform the motion and force of a clump between local and global coordinates. The Hertz–Mindlin elastic contact force model, incorporated with the nonlinear normal viscous force and the Mohr–Coulomb friction law, is used to describe the interactions between particles. The proposed discrete element model is used to simulate direct shear tests of the irregular limestone rubbles. The simulation results of vertical displacements and shear stresses with a mixture of clumps are compared well with that of laboratory tests. The bulk friction coefficients are calculated and discussed under different contact friction coefficients and normal stresses. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Application of a wheel–rail contact model to railway dynamics in small radius curved tracks

A multibody formulation with Cartesian coordinates is used to describe the kinematic structure of rigid bodies and joints that constitute the vehicle. A track parameterization methodology is implemented for the accurate description of the track spatial geometry emphasizing small radius curves, including its irregularities. A generic formulation is reviewed to determine, during the dynamic analysis, the contact forces that are generated in the wheel–rail interface. This contact model includes an algorithm that identifies the coordinates of the wheel–rail contact points, even for the most general three dimensional motion of the wheelset on the track. The proposed formulation can be applied to study the two points of contact scenario and, since the contact point in the wheel flange does not have to be located in the same plane as the contact point in the tread, it allows analyzing lead and lag flange contact configurations. An elastic force model that allows computing of the normal contact force in the wheel–rail interface, accounting for the energy loss during contact, is implemented and the tangential wheel–rail contact forces are calculated using one of three distinct creep force models: Kalker linear theory; Heuristic nonlinear method; Polach formulation. The methodologies proposed here are demonstrated by their application to the dynamic analysis of the boggie of a metro rail vehicle when negotiating a small radius curved track.

ロボットハンドによる把持・操り動作を実現する半球型ソフトフィンガの幾何学的・材料学的非線形性を考慮した弾性力モデル

This study focuses on the derivation of elastic force models of a hemispherical soft fingertip and reveals the existence of a local minimum of elastic potential energy (LMEE) induced by the deformation of the fingertip. The proposed model can be written in a straightforward equation when the geometric nonlinearity of the fingertip is applied in the derivation process, which is suitable for analyzing the stability of robotic handling system with soft fingertips. We also show complete elastic force and potential energy equations by incorporating the material nonlinearity into the derived model. Furthermore, we compare our models with the Hertzian contact theory that is applicable to the practical usage for the strength design of a lot of machines. Finally, we demonstrate the validity of our models by comparing simulation results and experimental results.

On the Modeling and Analysis of Machining Performance in Micro-Endmilling, Part II: Cutting Force Prediction

In Part II of this paper, a cutting force model for the micro-endmilling process is developed. This model incorporates the minimum chip thickness concept in order to predict the effects of the cutter edge radius on the cutting forces. A new chip thickness computation algorithm is developed to include the minimum chip thickness effect. A slip-line plasticity force model is used to predict the force when the chip thickness is greater than the minimum chip thickness, and an elastic deformation force model is employed when the chip thickness is less than the minimum chip thickness. Orthogonal, microstructure-level finite element simulations are used to calibrate the parameters of the force models for the primary metallurgical phases, ferrite and pearlite, of multiphase ductile iron workpieces. The model is able to predict the magnitudes of the forces for both the ferrite and pearlite workpieces as well as for the ductile iron workpieces within 20%.

Description of Elastic Forces in Absolute Nodal Coordinate Formulation

The objective of this paper is to investigate the accuracy of the elastic force models that can be used in the absolute nodal coordinate finite element formulation. This study focuses on the description of the elastic forces in three-dimensional beams. The elastic forces of the absolute nodal coordinate formulation can be derived using a continuum mechanics approach. This study investigates the accuracy and usability of such an approach for a three-dimensional absolute nodal coordinate beam element. This study also presents an improvement proposal for the use of a continuum mechanics approach in deriving the expression of the elastic forces in the beam element. The improvement proposal is verified using several numerical examples that show that the proposed elastic force model of the beam element agrees with the analytical results as well as with the solutions obtained using existing finite element formulation. In the beam element under investigation, global displacements and slopes are used as the nodal coordinates, which resulted in a large number of nodal degrees of freedom. This study provides a physical interpretation of the nodal coordinates used in the absolute nodal coordinate beam element. It is shown that a beam element based on the absolute nodal coordinate formulation relaxes the assumption of a rigid cross-section and is capable of representing a distortional deformation of the cross-section. The numerical results also imply that the beam element does not suffer from the phenomenon called shear locking.

Development of elastic force model for wheel/rail contact problems

In this investigation, a new formulation for the wheel/rail contact problem based on the elastic force approach is presented. Crucial to the success of any elastic force formulation for the wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing additional differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length travelled by the wheel set. In the formulation presented in this paper, four parameters are used to describe the wheel and the rail surfaces. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.

DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION

The objective of this study is to develop simple and accurate elastic force models that can be used in the absolute nodal co-ordinate formulation for the analysis of two-dimensional beams. These force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach, without the need for introducing a local element co-ordinate system. Four new different force models that include different degrees of complexity are presented. It is shown that the vector of the elastic forces can be significantly simplified as compared to the elastic force model developed for the absolute nodal co-ordinate formulation using a local element frame [1]. Despite the simplicity of the new models, they account for elastic non-linearity in the strain–displacement relationship. Therefore, they lead to more accurate results as compared to the more complex models developed using the local frame method which does not account for the non-linearities in the strain–displacement relationships. Numerical results are presented in order to demonstrate the use of the new models and test their performances in the analysis of large deformations of flexible multibody systems.

Reconstitution and electron paramagnetic resonance-spectroscopic characterization of glycophorin containing phospholipid vesicles

Glycophorin A containing dimyristoylphosphatidylcholine vesicles has been reconstituted by reverse-phase evaporation, detergent dialysis, freeze and thaw cycles as well as by rehydration of a lipid-protein-film. The availability of each method has been tested. Reproducible results with a highly purified protein were only obtained by the reverse phase evaporation and the detergent dialysis techniques. The lipid-protein interaction was studied by electron spin resonance experiments using spin labeled phosphatidylcholine (PC-SL), phosphatidylglycerol (PG-SL) and phosphatidylethanolamine (PE-SL) as probe molecules. With PC-SL we observed protein-induced motionally restricted lipid, which is stable up to 40°C in DMPC-membranes. This rigidification in the fluid phase was already obtained at very low glycophorin content. It is interpretable with an elastic force model, where the membrane distortion is induced by a mismatch of lipid and protein hydrophobic thickness. Negatively charged PG-SL undergoes an additional electrostatic interaction leading to a preferential binding over PC-SL. With PE-SL we failed to observe motionally restricted lipid. However, the probe becomes diffusionally restricted in fluid bilayer membranes probably by hydrogen bond formation.

Analysis of the Grüneisen parameters of some fcc metals by an improved elastic force model

An analysis of the temperature dependence of Grüneisen parameters of copper, silver, gold, and aluminium is performed in terms of the elastic constants and their pressure derivatives by a new lattice dynamical model. The model satisfies the symmetry requirements of the lattice and the lattice is in equilibrium without recourse to external forces. The microscopic Grüneisen parameters gq,j are calculated as a function of wave vector q, along the principal symmetry directions, (100), (110), (111), (210), (211), and (221), and the values are averaged over the wave vector space in the first Brillouin zone. For the evaluation of integrals, the modified Houston’s method is used. The Grüneisen parameters computed in our present study show reasonably satisfactory agreement with experimental measurements.

Debye‐waller factors for rare gas solids

AbstractMean‐square displacements of the rare gas solids (Ne, Ar, Kr, and Xe) are calculated as a function of temperature, using eigenvalues as obtained from the unpaired elastic force model, recently developed. The present results are compared with the theoretical results of Goldman, because of the paucity of experimental results. Lindemann's melting criterion is tested by evaluating the ratio of the root‐mean‐square displacement to the nearest neighbour distance. It is observed that this ratio is almost constant for all rare gas solids.

The Lattice Dynamics of Quantum Crystals of F.C.C. 4He

AbstractThe lattice dynamics of solid helium in the f.c.c. phase is investigated using an unpaired elastic force model (EFM). The potential energy of the crystal is assumed to be made up of two parts: (1) the potential energy, giving rise to the central (pair‐wise) forces and 2. that one, giving rise to the unpaired forces. The model parameters are calculated using five experimental phonon frequencies. The frequency spectruy calculated at all the irreducible points of the first Brillouin zone is further used to compute the phonon density of states, lattice heat capacities, and Debye characteristic temperatures. The use of the model parameters is also made to predict the experimentally unavailable elastic constants in the f.c.c. phase. The theoretical results for the phonon frequencies along [100], [110], and [111] symmetry directions compare well with recent available experimental data.