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

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.

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Influence of cheese ripening on the viscoelastic behaviour of edam cheese

Czech Journal of Food Sciences ◽

10.17221/6566-cjfs ◽

2013 ◽

Vol 19 (No. 1) ◽

pp. 1-7 ◽

Cited By ~ 1

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.

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

Shock and Vibration ◽

10.1155/2014/709367 ◽

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.

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Linear viscoelastic boundary element formulation for steady state moving loads

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2003.10.005 ◽

2004 ◽

Vol 28 (7) ◽

pp. 815-823 ◽

Cited By ~ 10

Author(s):

José A González ◽

Ramón Abascal

Keyword(s):

Steady State ◽

Boundary Element ◽

Element Formulation ◽

Moving Loads ◽

Linear Viscoelastic

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Linear viscoelasticity

Continuum Mechanics of Solids ◽

10.1093/oso/9780198864721.003.0029 ◽

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.

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

European Journal of Wood and Wood Products ◽

10.1007/s00107-020-01566-1 ◽

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.

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

Journal of Applied Mechanics ◽

10.1115/1.3641792 ◽

1961 ◽

Vol 28 (4) ◽

pp. 611-617 ◽

Cited By ~ 128

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.

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

Mathematics ◽

10.3390/math9182333 ◽

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.

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