A Triboelastic Model for the Cyclic Mechanical Behavior of Filled Vulcanizates

1995 ◽  
Vol 68 (4) ◽  
pp. 660-670 ◽  
Author(s):  
V. A. Coveney ◽  
D. E. Johnson ◽  
D. M. Turner
Keyword(s):  
Natural Rubber ◽  
Mechanical Behavior ◽  
Material Behavior ◽  
Computationally Efficient ◽  
Complex Deformation ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Basic Equations ◽  
Efficient Approximation ◽  
Natural Rubber Vulcanizates

Abstract Aspects of the mechanical behavior of filled vulcanizates are reviewed with reference to existing mathematical models. The basic equations of the triboelastic theory, previously described by Turner, are derived. A standard triboelastic solid (STS) three parameter model, analogous to the standard linear solid, is described and a computationally efficient approximation developed. Comparisons are made between the predictions of the STS model and the behavior of testpieces of heavily filled natural rubber vulcanizates when subjected to simple and to complex deformation histories at various frequencies; the model is found to give a satisfactory representation of material behavior. Limitations of the STS model are also discussed.

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.

scholarly journals Mechanical Behavior of Axonal Microtubules; the Effect of Fluid on the Rupture of Axonal Microtubules

2018 ◽  
Author(s):  
Farid Manuchehrfar ◽  
Amir Shamloo
Keyword(s):  
Mechanical Behavior ◽  
Tau Protein ◽  
Random Number ◽  
Average Length ◽  
Tau Proteins ◽  
Particle Dynamic ◽  
Vital Importance ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Cross Links

AbstractAxonal microtubules are dynamically instable bundles in the interior part of the axon. The dynamics of these bundles are of vital importance in the behavior of axon such as their degeneration. Each axon typically contains 10~100 microtubule bundles with average length of 4μm. These bundles are coated with cytoplasm and are cross linked with random number of tau proteins. In some circumstances such as acceleration or deceleration of head in space or during the strike, they are placed in tension which may cause rupture of these bundles or disconnection of tau protein cross links. Mechanical behavior and rupture modality of microtubule bundles are becoming more and more important recently. In our model, viscoelastic microtubule bundles constituted from several discrete masses connected to the neighboring mass with a standard linear solid (SLS), a spring damper model. In addition we take into account the effect of cytoplasm by Dissipative Particle Dynamic (DPD) to investigate the rupture nature and mechanical behavior of these bundles and the effect of cytoplasm on their mechanical behavior. We obtain these results for various amounts of suddenly applied end forces to the group of axonal microtubule bundles.

scholarly journals Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

2016 ◽  
Vol 7 ◽  
pp. 554-571 ◽  
Author(s):  
Santiago D Solares
Keyword(s):  
Atomic Force Microscopy ◽  
Computational Study ◽  
Plane Surface ◽  
Material Behavior ◽  
Dynamic Mode ◽  
Viscoelastic Materials ◽  
Force Microscopy ◽  
Atomic Force ◽  
Standard Linear Solid ◽  
Standard Linear

Significant progress has been accomplished in the development of experimental contact-mode and dynamic-mode atomic force microscopy (AFM) methods designed to measure surface material properties. However, current methods are based on one-dimensional (1D) descriptions of the tip–sample interaction forces, thus neglecting the intricacies involved in the material behavior of complex samples (such as soft viscoelastic materials) as well as the differences in material response between the surface and the bulk. In order to begin to address this gap, a computational study is presented where the sample is simulated using an enhanced version of a recently introduced model that treats the surface as a collection of standard-linear-solid viscoelastic elements. The enhanced model introduces in-plane surface elastic forces that can be approximately related to a two-dimensional (2D) Young’s modulus. Relevant cases are discussed for single- and multifrequency intermittent-contact AFM imaging, with focus on the calculated surface indentation profiles and tip–sample interaction force curves, as well as their implications with regards to experimental interpretation. A variety of phenomena are examined in detail, which highlight the need for further development of more physically accurate sample models that are specifically designed for AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information.

Mechanical behavior of porcine thoracic aorta in physiological and supra-physiological intraluminal pressures

2017 ◽  
Vol 231 (4) ◽  
pp. 326-336 ◽  
Author(s):  
Mobin Rastgar Agah ◽  
Kaveh Laksari ◽  
Soroush Assari ◽  
Kurosh Darvish
Keyword(s):  
Constitutive Model ◽  
Mechanical Behavior ◽  
Pressure Range ◽  
Axial Loading ◽  
Outer Wall ◽  
Stretch Ratio ◽  
Material Behavior ◽  
Three Dimensions ◽  
Computationally Efficient ◽  
Custom Made

Understanding the mechanical behavior of aorta under supra-physiological loadings is an important aspect of modeling tissue behavior in various applications that involve large deformations. Utilizing inflation–extension experiments, the mechanical behavior of porcine descending thoracic aortic segments under physiological and supra-physiological intraluminal pressures was investigated. The pressure was changed in the range of 0–70 kPa and the deformation of the segment was determined in three dimensions using a custom-made motion capture system. An orthotropic Fung-type constitutive model was characterized by implementing a novel computationally efficient framework that ensured material stability for numerical simulations. The nonlinear rising trend of circumferential stretch ratio [Formula: see text] from outer toward inner wall was significantly increased at higher pressures. The increase in [Formula: see text] from physiological pressure (13 kPa) to 70 kPa was 13% at the outer wall and 22% at the inner wall; in this pressure range, the longitudinal stretch ratio [Formula: see text] increased 20%. A significant nonlinearity in the material behavior was observed as in the same pressure range, and the circumferential and longitudinal Cauchy stresses at the inner wall were increased 16 and 18 times, respectively. The overall constitutive model was verified in several loading paths in the [Formula: see text] space to confirm its applicability in multi-axial loading conditions.

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.

Visco-Elasticity of Passive Cardiac Muscle

1980 ◽  
Vol 102 (1) ◽  
pp. 57-61 ◽  
Author(s):  
J. G. Pinto ◽  
P. J. Patitucci
Keyword(s):  
Mechanical Behavior ◽  
Cardiac Muscle ◽  
Heart Muscle ◽  
Relaxation Times ◽  
Continuous Distribution ◽  
Biological Tissues ◽  
Constitutive Law ◽  
Strain Behavior ◽  
Standard Linear Solid ◽  
Standard Linear

A quantitative mechanical description of the heart organ requires information on the mechanical behavior of its muscle in reasonable unity and completeness. In this respect, a fundamental constitutive law for soft biological tissues was proposed by Fung in 1972. This article presents evidence to show that Fung’s law is a useful law to describe the mechanical behavior of heart muscle in the unstimulated (diastolic) state with sufficient generality. A visco-elastic relaxation phenomenon is studied in the isolated cardiac muscle of cat and rabbit with the purpose of constructing a mathematical model for relaxation. Experimental results show that passive relaxation behavior of heart muscle can be adequately described by a generalized standard linear solid with a continuous distribution of relaxation times. The form of the relaxation function devised permits the application of linear visco-elasticity theory to the nonlinear cardiac muscle. The relaxation model is used to predict the force-length (stress-strain) behavior of papillary muscle with reasonable accuracy.

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 Material parametrization of natural rubber based compound and characterization of crack propagation under consideration of dissipative effects

2021 ◽  
Author(s):  
Dan Pornhagen ◽  
Konrad Schneider ◽  
Markus Stommel
Keyword(s):  
Energy Dissipation ◽  
Crack Propagation ◽  
Natural Rubber ◽  
Experimental Tests ◽  
Material Behavior ◽  
Prony Series ◽  
Material Forces ◽  
Cracking Behavior ◽  
Dissipative Effects

AbstractMost concepts to characterize crack propagation were developed for elastic materials. When applying these methods to elastomers, the question is how the inherent energy dissipation of the material affects the cracking behavior. This contribution presents a numerical analysis of crack growth in natural rubber taking energy dissipation due to the visco-elastic material behavior into account. For this purpose, experimental tests were first carried out under different load conditions to parameterize a Prony series as well as a Bergström–Boyce model with the results. The parameterized Prony series was then used to perform numerical investigations with respect to the cracking behavior. Using the FE-software system ANSYS and the concept of material forces, the influence and proportion of the dissipative components were discussed.

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