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 Influence of cheese ripening on the viscoelastic behaviour of edam cheese

2013 ◽  
Vol 19 (No. 1) ◽  
pp. 1-7 ◽  
Author(s):  
J. Buchar ◽  
I. Kubiš ◽  
S. Gajdůšek ◽  
I. Křivánek
Keyword(s):  
Viscoelastic Properties ◽  
Rheological Model ◽  
Deformation Behaviour ◽  
Viscoelastic Body ◽  
Original Method ◽  
Cheese Ripening ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Pressure Bar

The paper deals with the study of the effect of cheese ripening on parameters of a rheological model of cheese mechanical behaviour. The Edam cheese has been tested by the method of the Hopkinson Split Pressure Bar. The original method of the evaluation of viscoelastic properties has been used. The rheological model of the three element linear viscoelastic body, so called “standard linear solid” has been used. This model successfully describes the experimentally observed deformation behaviour of cheese specimens. The effect of the time of cheese ripening on the parameters of the rheological model has been demonstrated.

scholarly journals Viscoelastic Characterization of Long-Eared Owl Flight Feather Shaft and the Damping Ability Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jia-li Gao ◽  
Jin-kui Chu ◽  
Le Guan ◽  
Hai-xin Shang ◽  
Zhen-kun Lei
Keyword(s):  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Golden Eagle ◽  
Flight Feather ◽  
Column Material ◽  
Significant Difference ◽  
Single Column ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear

Flight feather shaft of long-eared owl is characterized by a three-parameter model for linear viscoelastic solids to reveal its damping ability. Uniaxial tensile tests of the long-eared owl, pigeon, and golden eagle flight feather shaft specimens were carried out based on Instron 3345 single column material testing system, respectively, and viscoelastic response of their stress and strain was described by the standard linear solid model. Parameter fitting result obtained from the tensile tests shows that there is no significant difference in instantaneous elastic modulus for the three birds’ feather shafts, but the owl shaft has the highest viscosity, implying more obvious viscoelastic performance. Dynamic mechanical property was characterized based on the tensile testing results. Loss factor (tanδ) of the owl flight feather shaft was calculated to be 1.609 ± 0.238, far greater than those of the pigeon (0.896 ± 0.082) and golden eagle (1.087 ± 0.074). It is concluded that the long-eared owl flight feather has more outstanding damping ability compared to the pigeon and golden eagle flight feather shaft. Consequently, the long-eared owl flight feathers can dissipate the vibration energy more effectively during the flying process based on the principle of damping mechanism, for the purpose of vibration attenuation and structure radiated noise reduction.

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 Creep in oak material from the Vasa ship: verification of linear viscoelasticity and identification of stress thresholds

2020 ◽  
Vol 78 (6) ◽  
pp. 1095-1103
Author(s):  
R. Afshar ◽  
M. Cheylan ◽  
G. Almkvist ◽  
A. Ahlgren ◽  
E. K. Gamstedt
Keyword(s):  
Rheological Parameters ◽  
Stress Strain ◽  
Compressive Stresses ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Linear Viscoelastic Behaviour ◽  
Creep Deformations ◽  
High Degree ◽  
Wooden Structures

Abstract Creep deformation is a general problem for large wooden structures, and in particular for shipwrecks in museums. In this study, experimental creep data on the wooden cubic samples from the Vasa ship have been analysed to confirm the linearity of the viscoelastic response in the directions where creep was detectable (T and R directions). Isochronous stress–strain curves were derived for relevant uniaxial compressive stresses within reasonable time spans. These curves and the associated creep compliance values justify that it is reasonable to assume a linear viscoelastic behaviour within the tested ranges, given the high degree of general variability. Furthermore, the creep curves were fitted with a one-dimensional standard linear solid model, and although the rheological parameters show a fair amount of scatter, they are candidates as input parameters in a numerical model to predict creep deformations. The isochronous stress–strain relationships were used to define a creep threshold stress below which only negligible creep is expected. These thresholds ranges were 0.3–0.5 MPa in the R direction and 0.05–0.2 MPa in the T direction.

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.

scholarly journals Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

2015 ◽  
Vol 6 ◽  
pp. 369-379 ◽  
Author(s):  
Horacio V Guzman ◽  
Pablo D Garcia ◽  
Ricardo Garcia
Keyword(s):  
Viscoelastic Model ◽  
Surface Force ◽  
Dissipated Energy ◽  
Dynamic Force ◽  
Force Microscopy ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Optimal Accuracy ◽  
The One

We present a simulation environment, dForce, which can be used for a better understanding of dynamic force microscopy experiments. The simulator presents the cantilever–tip dynamics for two dynamic AFM methods, tapping mode AFM and bimodal AFM. It can be applied for a wide variety of experimental situations in air or liquid. The code provides all the variables and parameters relevant in those modes, for example, the instantaneous deflection and tip–surface force, velocity, virial, dissipated energy, sample deformation and peak force as a function of time or distance. The simulator includes a variety of interactions and contact mechanics models to describe AFM experiments including: van der Waals, Hertz, DMT, JKR, bottom effect cone correction, linear viscoelastic forces or the standard linear solid viscoelastic model. We have compared two numerical integration methods to select the one that offers optimal accuracy and speed. The graphical user interface has been designed to facilitate the navigation of non-experts in simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years.

Linear Viscoelastic Creep Model for the Contact of Nominal Flat Surfaces Based on Fractal Geometry: Standard Linear Solid (SLS) Material

2007 ◽  
Vol 129 (3) ◽  
pp. 461-466 ◽  
Author(s):  
Osama M. Abuzeid ◽  
Peter Eberhard
Keyword(s):  
Constitutive Law ◽  
Creep Model ◽  
Viscoelastic Creep ◽  
Flat Surfaces ◽  
Proposed Model ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Creep Force ◽  
Good Agreement

The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The material’s behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.

Modeling of Tread Block Contact Mechanics Using Linear Viscoelastic Theory3

2008 ◽  
Vol 36 (3) ◽  
pp. 211-226 ◽  
Author(s):  
F. Liu ◽  
M. P. F. Sutcliffe ◽  
W. R. Graham
Keyword(s):  
High Speed ◽  
Slip Rate ◽  
Material Model ◽  
Contact Forces ◽  
Block Modeling ◽  
Rate Dependent ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
The Impact ◽  
Good Agreement

Abstract In an effort to understand the dynamic hub forces on road vehicles, an advanced free-rolling tire-model is being developed in which the tread blocks and tire belt are modeled separately. This paper presents the interim results for the tread block modeling. The finite element code ABAQUS/Explicit is used to predict the contact forces on the tread blocks based on a linear viscoelastic material model. Special attention is paid to investigating the forces on the tread blocks during the impact and release motions. A pressure and slip-rate-dependent frictional law is applied in the analysis. A simplified numerical model is also proposed where the tread blocks are discretized into linear viscoelastic spring elements. The results from both models are validated via experiments in a high-speed rolling test rig and found to be in good agreement.

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.

Sign in / Sign up

Export Citation Format

Share Document