Frictional Sliding on a Constrained Rubber Layer: A Simple Model for a Class of Damping Devices

2000 ◽  
Vol 73 (2) ◽  
pp. 205-216
Author(s):  
C. G. Li ◽  
P. S. Steif
Keyword(s):  
Simple Model ◽  
Nonlinear Behavior ◽  
Constitutive Law ◽  
Dynamic Moduli ◽  
Approximate Methods ◽  
Rubber Layer ◽  
New Class ◽  
Industrial Grade ◽  
Dependent Behavior ◽  
Filled Rubbers

Abstract Resistance to the steady sliding of a cylinder over a thin rubber layer is studied theoretically. This problem underlies a model being developed for a new class of damping devices. A quantitatively accurate model requires an accounting for the amplitude-dependent dynamic moduli of industrial-grade rubbers filled with carbon black. This accounting is hindered, however, by the lack of a full multiaxial constitutive law reflecting the nonlinear, amplitude-dependent behavior of filled rubbers. Accordingly, this paper sets forth approximate methods of analysis which indirectly account for the nonlinear behavior; these ultimately lead to compact solutions which can be used in the design of new devices.

Sliding Resistance on a Constrained Rubber Layer Due to Rubber Hysteresis

2000 ◽  
Vol 73 (2) ◽  
pp. 217-224
Author(s):  
C. G. Li ◽  
P. S. Steif
Keyword(s):  
Universal Design ◽  
Rolling Resistance ◽  
Design Tool ◽  
Constitutive Law ◽  
Rubber Layer ◽  
New Class ◽  
Dependent Behavior ◽  
Theoretical Predictions ◽  
Filled Rubbers ◽  
Sliding Resistance

Abstract Sliding resistance of a rigid cylinder over a thin rubber layer due to rubber hysteresis is investigated. This problem underlies a model being developed for quantitatively accurate predictions of the performance of a new class of damping devices. As a full multiaxial constitutive law reflecting the amplitude-dependent behavior of filled rubbers is not available, this paper sets forth an approximate method of analysis which indirectly accounts for the material nonlinearity. Results of extensive finite element calculations are then reduced to compact material-independent forms which can be used as a universal design tool. Measurements of rolling resistance are also compared with theoretical predictions.

Numerical analysis of history-dependent variational–hemivariational inequalities with applications to contact problems

2015 ◽  
Vol 26 (4) ◽  
pp. 427-452 ◽  
Author(s):  
MIRCEA SOFONEA ◽  
WEIMIN HAN ◽  
STANISŁAW MIGÓRSKI
Keyword(s):  
Numerical Analysis ◽  
Real World ◽  
Viscoelastic Body ◽  
Contact Problems ◽  
Uniqueness Result ◽  
Constitutive Law ◽  
Hemivariational Inequalities ◽  
New Class ◽  
Nonlinear Anal ◽  
Dependence Result

A new class of history-dependent variational–hemivariational inequalities was recently studied in Migórski et al. (2015Nonlinear Anal. Ser. B: Real World Appl.22, 604–618). There, an existence and uniqueness result was proved and used in the study of a mathematical model which describes the contact between a viscoelastic body and an obstacle. The aim of this paper is to continue the analysis of the inequalities introduced in Migórski et al. (2015Nonlinear Anal. Ser. B: Real World Appl.22, 604–618) and to provide their numerical analysis. We start with a continuous dependence result. Then we introduce numerical schemes to solve the inequalities and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modelled with a viscoelastic constitutive law, the contact is given in the form of normal compliance, and friction is described with a total slip-dependent version of Coulomb's law.

The nonlinear behavior of varicose disturbances in a simple model of the Gulf Stream

1991 ◽  
Vol 38 ◽  
pp. S591-S622 ◽  
Author(s):  
L.J. Pratt ◽  
J. Earles ◽  
P. Cornillon ◽  
J.-F. Cayula
Keyword(s):  
Simple Model ◽  
Gulf Stream ◽  
Nonlinear Behavior

Binder/Filler Interaction and the Nonlinear Behavior of Highly-Filled Elastomers

1990 ◽  
Vol 63 (4) ◽  
pp. 488-502 ◽  
Author(s):  
R. G. Stacer ◽  
C. Hübner ◽  
D. M. Husband
Keyword(s):  
Surface Area ◽  
Strain Amplitude ◽  
Nonlinear Response ◽  
Volume Fraction ◽  
Viscoelastic Behavior ◽  
Interaction Model ◽  
Nonlinear Behavior ◽  
Small Deformation ◽  
Amplitude Dependence ◽  
Filled Rubbers

Abstract 1. The small-deformation-viscoelastic response of elastomers containing nonreinforcing filler has been investigated. Nonlinear viscoelastic behavior was observed as a pronounced strain-amplitude dependence. The degree of this dependence was quantified using a power-law representation as a single nonlinear parameter, m. 2. The magnitude of m was a function of formulation variables. It was found that m increased with the volume fraction and particle size of filler material, as well as the volume fraction of plasticizer. Reduced values of m were observed in the presence of bonding agent and with greater degrees of apparent crosslinking. The latter was controlled in this study through imbalanced urethane cures. 3. Nonlinear behavior of elastomers containing nonreinforcing filler has been compared and contrasted with the data base for carbon-black-reinforced elastomers. The major difference is in the effect of the surface area of filler particles. Nonlinear response in black-filled rubbers increases with surface area, while the opposite is reported in this study. Additionally, the relationship between viscoelastic dissipation and the magnitude of nonlinear response, well established for black-filled rubbers, was not observed. These results indicate that the response of elastomers containing nonreinforcing filler, although nearly identical in appearance to that seen with reinforcing filler, is not driven by the same mechanism. 4. A binder/filler interaction model is proposed for materials containing nonreinforcing filler. This model is based on the ideal adhesive strength of the binder/filler interface. In this model, greater attraction between polymer and particle surfaces reduces molecular slippage during deformation, leading to a decreased dependence of the modulus on strain amplitude, or decreased nonlinearity. It is shown that the model provides reasonable predictions for the observed phenomena.

Phenomenological Mechanism of Transformation Plasticity and the Constitutive Law Coupled with Thermo-Mechanical Plasticity

2008 ◽  
Vol 33-37 ◽  
pp. 1351-1358 ◽  
Author(s):  
Tatsuo Inoue
Keyword(s):  
Plastic Deformation ◽  
Phase Transformation ◽  
Simple Model ◽  
Constitutive Equation ◽  
Yield Function ◽  
Constitutive Law ◽  
Strain Rates ◽  
Strain Response ◽  
Transformation Plasticity ◽  
New Phase

Phenomenological mechanism of transformation plasticity is proposed in the first part of the paper by use of simple model why stress in mother phase increases to reach yielding due to progressing new phase and to induce plastic deformation even under small applied stress. Based on the discussion, a unified constitutive model including transformation-induced and ordinal thermomechanical plastic strain rates by introducing an effect of varying phases during phase transformation into yield function. Thus derived constitutive equation is applied to describe strain response under varying temperature and stress with some discussions as well as metallo-thermo-mechanical simulation of quenching.

Chebyshev Polynomials Fits for Efficient Analysis of Finite Length Squeeze Film Damped Rotors

2002 ◽  
Vol 125 (1) ◽  
pp. 175-183 ◽  
Author(s):  
F. A. Rodrigues ◽  
F. Thouverez ◽  
C. Gibert ◽  
L. Jezequel
Keyword(s):  
Steady State ◽  
Finite Length ◽  
Pressure Field ◽  
Fluid Pressure ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Squeeze Film ◽  
Approximate Methods ◽  
Squeeze Film Dampers ◽  
The Time Domain

The nonlinear behavior of the hydrodynamic forces generated by squeeze film dampers makes dynamical analyses of rotor-bearing systems incorporating such devices a complex and often long task. When steady-state orbits are to be sought, approximate methods (e.g., harmonic balance method, trigonometric collocation method) can be used in order to save computation cost. However, numerical integration in the time domain cannot be avoided if one wishes to calculate transient responses, or to carry out more meticulous analyses concerning the effects of the damper nonlinear nature on the motion of the system. For finite length squeeze film dampers, neither the short nor the long bearing approximations can be suitably applied, and the fluid pressure field has to be estimated numerically, thus rendering rotordynamics predictions even longer and, for engineering purposes computationally prohibitive. To surmount this problem, the present paper proposes a straightforward procedure to derive polynomial expressions for the squeeze film damper (SFD) forces, for given damper geometry and boundary conditions. This is achieved by applying Chebyshev orthogonal polynomial fits over force data generated by numerically solving the two-dimensional pressure field governing equation. For both transient and steady-state calculations, the use of the SFD forces polynomial expressions is seen to be very efficient and precise.

Development of Time Dependent Stress-Strain Simulation of Clay

2009 ◽  
Vol 25 (1) ◽  
pp. 27-40 ◽  
Author(s):  
C.-Y. Ou ◽  
C.-C. Liu ◽  
C.-K. Chin
Keyword(s):  
Constitutive Law ◽  
Time Dependent ◽  
Soil Behavior ◽  
Creep Tests ◽  
Clay Model ◽  
Model Sets ◽  
Dependent Behavior ◽  
Modified Cam Clay ◽  
Parametric Studies ◽  
Cam Clay

AbstractThe objective of this study is to derive a time dependent effective based constitutive law on the basis of framework of the Modified Cam-Clay model. This model takes into account the anisotropic characteristics and creep behavior, based on the theory of viscoplasticity. The model sets the initial yield surface symmetric to the Ko line for modeling the initial Ko condition. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress gyration after shear. The creep or time dependent behavior is considered in the model by adopting Kutter and Sathialingam's model, which was derived from Taylor's secondary consolidation theory and Bjerrum's delayed compression model. Compared with the Modified Cam-Clay model, the model requires five additional parameters to describe the soil behavior. All of the additional parameters can be obtained through conventional soil tests or parametric studies. The model is evaluated through a series of simulation of undrained shear tests and undrained creep tests.

Solution Methods for a New Class of Simple Model Neurons

2007 ◽  
Vol 19 (12) ◽  
pp. 3216-3225 ◽  
Author(s):  
Mark D. Humphries ◽  
Kevin Gurney
Keyword(s):  
Simple Model ◽  
Neuron Model ◽  
Solution Method ◽  
Cortical Cell ◽  
Spike Generation ◽  
Firing Patterns ◽  
New Class ◽  
Efficient Simulation ◽  
Different Types ◽  
Solution Methods

Izhikevich (2003) proposed a new canonical neuron model of spike generation. The model was surprisingly simple yet able to accurately replicate the firing patterns of different types of cortical cell. Here, we derive a solution method that allows efficient simulation of the model.

Electric Polarization Caused by a Diffusion Flow in a Polar Gas Mixture

1974 ◽  
Vol 29 (3) ◽  
pp. 373-375
Author(s):  
S. Hess
Keyword(s):  
Simple Model ◽  
Kinetic Theory ◽  
Electric Polarization ◽  
Constitutive Law ◽  
Gas Mixture ◽  
Diffusion Flow ◽  
Collision Integrals ◽  
Thermo Electric ◽  
Previously Treated ◽  
Symmetric Top Molecules

The kinetic theory of the diffusio-electric polarization is developed analogous to the previously treated thermo-electric polarization (Waldmann, Hess 1969). The relevant constitutive law is derived. The characteristic coefficient determining the magnitude of this effect is related to collision integrals obtained from the Waldmann-Snider equation. A simple model calculation shows that this coefficient will be nonzero, in general, and of measurable size, for polar symmetric top molecules

scholarly journals An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

2019 ◽  
Vol 19 (2) ◽  
pp. 633-659 ◽  
Author(s):  
Adrienne Propp ◽  
Alessio Gizzi ◽  
Francesc Levrero-Florencio ◽  
Ricardo Ruiz-Baier
Keyword(s):  
Cardiac Tissue ◽  
Viscoelastic Model ◽  
Constitutive Law ◽  
Governing Equations ◽  
Finite Element Scheme ◽  
Additional Degree ◽  
Active Strain ◽  
New Class ◽  
Calcium Interaction ◽  
Coupling Mechanisms

Abstract We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law, for both active stress and active strain formulations of active mechanics, coupled with a four-variable phenomenological model for human cardiac cell electrophysiology, which produces an accurate description of the action potential. The conductivities in the model of electric propagation are modified according to stress, inducing an additional degree of nonlinearity and anisotropy in the coupling mechanisms, and the activation model assumes a simplified stretch–calcium interaction generating active tension or active strain. The influence of the new terms in the electromechanical model is evaluated through a sensitivity analysis, and we provide numerical validation through a set of computational tests using a novel mixed-primal finite element scheme.

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