The Rolling Contact of a Rigid Cylinder With a Viscoelastic Half Space

1961 ◽  
Vol 28 (4) ◽  
pp. 611-617 ◽  
Author(s):  
S. C. Hunter
Keyword(s):  
Elastic Problem ◽  
Rolling Contact ◽  
Inertial Forces ◽  
Viscoelastic Solid ◽  
Rolling Velocity ◽  
Rigid Cylinder ◽  
Viscoelastic Effects ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Intermediate Value

The problem of a rigid cylinder rolling on the surface of a viscoelastic solid is solved in an approximation in which inertial forces are neglected. With the introduction of viscoelastic effects, the symmetry associated with the corresponding elastic problem is destroyed, and in particular the cylinder motion is impeded by a resistive force. For a standard linear solid, the resulting coefficient of friction, a function of the rolling velocity V, tends to zero for small and large values of V, and attains a single maximum at an intermediate value.

Modeling of Viscoelastic Solid Polymers Using a Boundary Element Formulation with Considering a Body Load

2012 ◽  
Vol 463-464 ◽  
pp. 499-504 ◽  
Author(s):  
Hosein Ashrafi ◽  
M.R. Bahadori ◽  
M. Shariyat
Keyword(s):  
Boundary Element ◽  
Body Force ◽  
Element Formulation ◽  
Viscoelastic Solid ◽  
Engineering Structures ◽  
Solid Polymers ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Body Load ◽  
Standard Linear

In this work, a boundary element formulation for 2D linear viscoelastic solid polymers subjected to body force of gravity has been presented. Structural analysis of solid polymers is one of the most important subjects in advanced engineering structures. From basic assumptions of the viscoelastic constitutive equations and the weighted residual techniques, a simple but effective boundary element formulation is implemented for standard linear solid (SLS) model. The SLS model provides an approximate representation of observed behavior of a real advanced polymer in its viscoelastic range. This approach avoids the use of relaxation functions and mathematical transformations, and it is able to solve quasistatic viscoelastic problems with any load time-dependence and boundary conditions. Problem of pressurization of thick-walled viscoelastic tanks made of PMMA polymer, which subjected to a body force, is completely analyzed.

scholarly journals Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2333
Author(s):  
Ruslan Yanbarisov ◽  
Yuri Efremov ◽  
Nastasia Kosheleva ◽  
Peter Timashev ◽  
Yuri Vassilevski
Keyword(s):  
Free Surface ◽  
Viscoelastic Fluid ◽  
Fluid Model ◽  
Future Application ◽  
Solid Model ◽  
Multicellular Spheroids ◽  
Viscoelastic Solid ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Living Tissues

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.

Hysteresis and Viscoelastic Modeling of a Piezo-Optic Voltage Sensor

2008 ◽  
Author(s):  
Charles E. Seeley ◽  
Glen Koste ◽  
Craig Stringer
Keyword(s):  
Viscoelastic Model ◽  
Voltage Sensor ◽  
Sensor Technology ◽  
Optical Wave ◽  
Viscoelastic Effects ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Optical Wave Guide ◽  
Electro Magnetic ◽  
Viscoelastic Modeling

There is growing interest in sensor technology that is immune to electro-magnetic interference. By nature, development of this technology covers multiple physical domains including electronics, optics, mechanics and materials. This paper discusses development of a mathematical model to compensate for the hysteresis and viscoelastic effects of a piezo-optic voltage sensor. The sensor utilizes piezoelectric fibers with interdigitated electrodes coupled to an optical wave guide via a dielectric matrix. The unknown voltage energizes the piezoelectric fibers to deform fiber Bragg gratings (FBGs) on the waveguide. Therefore, a measurable change in wavelength is related to the unknown voltage. The hysteresis model is based on Rayleigh’s Law of magnetization that is adapted for the coupled piezoelectric and optic response, and the viscoelastic model is based on the standard linear solid model using springs and dashpots in combination. Model results compare favorably with experimental results.

Stress Analysis for Rolling Contact Between Two Viscoelastic Cylinders

1993 ◽  
Vol 60 (2) ◽  
pp. 310-317 ◽  
Author(s):  
Guangqiu Wang ◽  
K. Knothe
Keyword(s):  
Dry Friction ◽  
Rolling Resistance ◽  
Rolling Contact ◽  
Material Behavior ◽  
Two Dimensional ◽  
Space Theory ◽  
Standard Linear Solid ◽  
Steady State Rolling ◽  
Standard Linear ◽  
Contact Surfaces

The two-dimensional viscoelastic rolling contact with Coulomb’s dry friction is considered for steady-state rolling. A so-called standard linear solid (three parameter model) is used to characterize the viscoelastic material behavior. Rolling contact stresses between two rolling cylinders are investigated by a boundary element method, based on the half-space theory. Numerical results are presented including the stress distribution at the contact surfaces and in viscoelastic bodies as well as rolling resistance.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

2013 ◽  
Vol 399 (2) ◽  
pp. 472-479 ◽  
Author(s):  
Margareth S. Alves ◽  
Celene Buriol ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
Mauricio Sepúlveda ◽  
...  
Keyword(s):  
Asymptotic Behaviour ◽  
Thermal Effect ◽  
Solid Model ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear

scholarly journals Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1703
Author(s):  
Michael Coja ◽  
Leif Kari
Keyword(s):  
Natural Rubber ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Complex Problem ◽  
Wide Frequency Range ◽  
Vibration Isolators ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Frequency Magnitude ◽  
Good Agreement

A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag–Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.

Experimental identification of the material standard linear solid model parameters by means of dynamical measurements

2021 ◽  
pp. 107754632110371
Author(s):  
Stefano Amadori ◽  
Giuseppe Catania
Keyword(s):  
Frequency Domain ◽  
Solid Material ◽  
Model Parameters ◽  
Solid Model ◽  
Material Parameters ◽  
Experimental Identification ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Material Standard

A procedure for the experimental identification of the material standard linear solid model parameters by means of dynamic mechanical analysis test instrument measurements is presented. Since the standard linear solid material stress–strain functional D( ω) relationship in the frequency domain formally depends on the standard linear solid material parameters, a procedure able to identify these parameters from test measurement estimates is proposed in this work. Nevertheless, a critical, nonlinear and non-parametric approach is to be followed since the number of the material standard linear solid block components is generally unknown, and the material D( ω) shows a highly nonlinear dependency on the unknown standard linear solid material parameters. For these reasons, measurement and test model noise is expected to strongly influence the accuracy of the identification results. A multi-step procedure is presented, consisting first in the non-parametric identification of a frequency dependent, two degrees of freedom model instrument frame by means of a polynomial rational function, where polynomial order and parameters, such as polynomial coefficients and pole-residue couples, are optimally identified by means of an algebraic numerical technique and of an iterative stabilization procedure. Another procedure able to identify the material D( ω) polynomial rational functional relationship in the frequency domain is also proposed, taking into account the dynamic contribution of the instrument frame, of the inertial contribution of the distributed mass of the beam and of the lumped mass of the instrument force measuring system. An effective procedure, able to identify the standard linear solid material model parameters in the time domain from the identified material physical poles, is finally proposed. Some application examples, concerning the identification of the standard linear solid model of a known material and of an unknown composite material, are shown and discussed as well.

Viscoelastic Properties of Phagocytes in Arteriosclerotic Origin

2014 ◽  
Vol 540 ◽  
pp. 321-325
Author(s):  
Wei Zeng ◽  
Yan Rong Shi ◽  
Xiao Yan Deng
Keyword(s):  
Experimental Data ◽  
Viscoelastic Properties ◽  
Important Implication ◽  
Research Field ◽  
Solid Model ◽  
Initial Stage ◽  
Standard Linear Solid Model ◽  
Aspiration Technique ◽  
Standard Linear Solid ◽  
Standard Linear

A micropipette aspiration technique was adopted to investigate the viscoelastic properties of phagocytes of arteriosclerotic origin. A standard linear solid model was employed to fit the experimental data and three viscoelastic coefficients were used to compare the mechanical properties of the phagocytes in different phases during arteriosclerostic development. The experimental results indicated that prior to the formation of arteriosclerosis, the mobility and deformability of the marcopahges matured from monocytes decreased, and their rigidity increased. At the initial stage of arteriosclerosis formation, the mobility and deformability of the foam-cells further decreased. This finding may have important implication in the research field of arteriosclerosis.

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