Storage and loss stiffnesses and moduli as determined by dynamic nanoindentation

2009 ◽  
Vol 24 (3) ◽  
pp. 863-871 ◽  
Author(s):  
Wendelin J. Wright ◽  
W.D. Nix
Keyword(s):  
Physical Model ◽  
Composite System ◽  
Storage And Loss Moduli ◽  
In Series ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Load Frame ◽  
Composite Response ◽  
Dynamic Nanoindentation

The storage and loss stiffnesses for the composite response of the sample, indenter, and load frame during dynamic nanoindentation are derived. In the first part of the analysis, no physical model is assigned to the composite system. It is shown that this case is equivalent to the conventional nanoindentation analysis. In the second part of the analysis, the sample is modeled as a standard linear solid in series with the indenter and load frame. The results for the storage and loss stiffnesses as computed by the two methods differ by at most ∼3% for the elastomeric system under consideration. Results for the storage and loss moduli are also similar. The relative merits and weaknesses of each analysis are discussed.

Influence of the Internal State of a Maxwell Damper on Free Critically Damped Vibrations

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Physical Model ◽  
Initial Value Problems ◽  
Internal State ◽  
Initial Value ◽  
Zero Velocity ◽  
In Series ◽  
Standard Linear Solid ◽  
Standard Linear

A Maxwell damper with a damper spring in series with a viscous dashpot is a more physical model than a viscous dashpot because the Maxwell damper models the elasticity of the connecting links of the viscous dashpot. The system of a main spring in parallel with a Maxwell damper is known as the standard linear solid (SLS) in viscoelasticity. The response of this SLS attached to a mass for standard initial value problems: displacement (nonzero displacement with zero velocity) and velocity (zero displacement with nonzero velocity) have been analyzed a few times in the literature. However, different authors present different conclusions about the importance of modeling the damper spring. None of these authors have explored the influence of the initial internal state of the damper spring. Here it is shown that the initial internal state of the damper spring can significantly influence the response for both displacement and velocity initial value problems.

Comparison of 2-D numerical viscoelastic waveform modeling with ultrasonic physical modeling

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 862-871 ◽  
Author(s):  
Genmeng Chen
Keyword(s):  
Physical Model ◽  
Physical Modeling ◽  
Wave Attenuation ◽  
Numerical Study ◽  
Solid Model ◽  
Viscoelastic Materials ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Voigt Model

The objective of the study is to test the validity of theoretical models of wave attenuation by comparing their predictions of attenuation against physical model results. The study is confined to a 2-D geometry, and the viscoelastic materials used in physical modeling are those commonly used in the experiment. The physical modeling data of homogeneous media are compared with the numerical results in the frequency domain. The time‐domain comparisons between numerical modeling and physical modeling are also shown by three examples. The theoretical viscoelastic models used in the numerical study are the Kelvin‐Voigt model, the standard linear solid model, and the standard linear solid model with a continuous spectrum of relaxation time. On the comparison of a single model, all the models simulate the physical model fairly well, but the standard linear solid model gives the best result among them. The Kelvin‐Voigt model is easy to use as a quick first‐order simulation of the viscoelastic materials because it has fewer viscosity parameters than the other two models. The disadvantage of the Kelvin‐Voigt model is that it predicts too much attenuation of the high‐frequency components. It is also shown that neglecting the viscosity of some materials like polyvinylcloride plastic (PVC), which has high viscosity, will produce incorrect results in synthetic seismograms.

Linear viscoelasticity

2020 ◽  
pp. 549-608
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Time Integration ◽  
Integral Form ◽  
Essential Elements ◽  
Kernel Functions ◽  
Three Dimensions ◽  
Storage And Loss Moduli ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear

This chapter introduces the essential elements of linear viscoelastic material behaviour and modeling in one- and three-dimensions. Both relaxation and creep phenomena are introduced and modeled using Boltzmann’s superposition integral. Various common kernel functions are introduced, as is the standard and generalized standard linear model in differential and integral form. The correspondence principle is discussed for the solution of practical problems and to connect relaxation and creep formulations. Storage and loss moduli for oscillatory loadings are discussed, as are loss tangents and dissipation. For the generalized standard linear solid its time integration via the Herrmann-Peterson recursion relation is discussed. Effects of temperature are discussed, and the concept of time-temperature equivalence is introduced.

scholarly journals Recent Advancements in Fractal Geometric-Based Nonlinear Time Series Solutions to the Micro-Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

2011 ◽  
Vol 2011 ◽  
pp. 1-29 ◽  
Author(s):  
Osama M. Abuzeid ◽  
Anas N. Al-Rabadi ◽  
Hashem S. Alkhaldi
Keyword(s):  
Surface Roughness ◽  
Rough Surfaces ◽  
Power Laws ◽  
Experimental Models ◽  
Experimental Results ◽  
Closed Form Solutions ◽  
In Series ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Surface Creep

To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed-form solutions, are displayed graphically for selected values of the systems' parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro- and nano-electronic devices, circuits and systems.

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.

Investigation of the resonance amplitude of a standard linear solid

1975 ◽  
Vol 11 (2) ◽  
pp. 184-188
Author(s):  
Yu. I. Karkovskii ◽  
S. I. Meshkov
Keyword(s):  
Resonance Amplitude ◽  
Standard Linear Solid ◽  
Standard Linear
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