• Proceedings of the KSME Conference
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• 2000.04a
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• pp.280-285
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• 2000

A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed. The proposed model is derived through linearization of Simo's viscoelastic constitutive model and reference configuration transformation. The proposed constitutive equation is extended to a generalized viscoelastic constitutive equation that includes widely used Mormin's model as a special case using objective stress increment. Static deformation correction factor is introduced to consider the influence of Pre-strain on the relaxation function. The proposed constitutive model is tested fer dynamic behavior of rubber specimens with different carbon black contents. It is concluded from the test that the viscoelastic constitutive equation for filled rubber must include the influence of the static deformation on the time effects. The suggested constitutive equation with static deformation correction factor shows good agreement with test values.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.4
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• pp.619-628
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• 2001

A viscoelastic constitutive equation of rubber is proposed under small oscillatory load superimposed on large static deformation. The proposed model is derived through linearization of Simos nonlinear viscoelastic constitutive model and reference configuration transformation. Statically pre-deformed state is used as reference configuration. The model is extended to a generalized viscoelastic constitutive equation including widely-used Mormans model. Static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. The model is tested for dynamic behavior of rubbers with different carbon black fractions. It is shown that the constitutive equation with static deformation correction factor agrees well with test results.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.225-240
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• 1999

This paper presents a mechanistic approach to uniaxial viscoelastic constitutive modeling of asphalt concrete that accounts for damage evolution under cyclic loading conditions. An elasticviscoelastic correspondence principle in terms of pseudo variables is applied to separately evaluate viscoelasticity and time-dependent damage growth in asphalt concrete. The time-dependent damage growth in asphalt concrete is modeled by using a damage parameter based on a generalization of microcrack growth law. Internal state variables that describe the hysteretic behavior of asphalt concrete are determined. A constitutive equation in terms of stress and pseudo strain is first established for controlled-strain mode and then transformed to a controlled-stress constitutive equation by simply replacing physical stress and pseudo strain with pseudo stress and physical strain. Tensile uniaxial fatigue tests are performed under the controlled-strain mode to determine model parameters. The constitutive equations in terms of pseudo strain and pseudo stress satisfactorily predict the constitutive behavior of asphalt concrete all the way up to failure under controlled-strain and -stress modes, respectively.

• Proceedings of the Korean Fiber Society Conference
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• 1995.04a
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• pp.25-25
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• 1995

• Korea-Australia Rheology Journal
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• v.14 no.4
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• pp.161-174
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• 2002

A new technique for numerical calculation of viscoelastic flow based on the combination of Neural Net-works (NN) and Brownian Dynamics simulation or Stochastic Simulation Technique (SST) is presented in this paper. This method uses a "universal approximator" based on neural network methodology in combination with the kinetic theory of polymeric liquid in which the stress is computed from the molecular configuration rather than from closed form constitutive equations. Thus the new method obviates not only the need for a rheological constitutive equation to describe the fluid (as in the original Calculation Of Non-Newtonian Flows: Finite Elements St Stochastic Simulation Techniques (CONNFFESSIT) idea) but also any kind of finite element-type discretisation of the domain and its boundary for numerical solution of the governing PDE's. As an illustration of the method, the time development of the planar Couette flow is studied for two molecular kinetic models with finite extensibility, namely the Finitely Extensible Nonlinear Elastic (FENE) and FENE-Peterlin (FENE-P) models.P) models.

• Computational Structural Engineering
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• v.10 no.4
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• pp.229-238
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• 1997

Mechanical behavior of asphalt concrete that accounts for viscoelasticity and damage evolution under cyclic loading conditions is modeled and presented in this paper. An elastic-viscoelastic correspondence principle in terms of pseudo variables is applied to separately evaluate viscoelasticity and time-dependent damage growth in asphalt concrete. A microcrack growth law, which is commonly employed in linear viscoelastic fracture mechanics, is successfully used for describing the damage growth in the body. A constitutive equation in terms of stress and pseudo strain is first established for controlled-strain mode, and then transformed to controlled-stress constitutive equation by simply replacing stress and pseudo strain with pseudo stress and strain. The transformed constitutive equation in terms of pseudo stress satisfactorily predicts the mechanical behavior of asphalt concrete all the way up to failure under controlled-stress modes.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.937-956
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• 2014

The MEMS structures usually are made from silicon; consideration of the viscoelastic effect in microbeams duo to the phenomena of silicon creep is necessary. Application of the fractional model of microbeams made from viscoelastic materials is studied in this paper. Quasi-static and dynamical responses of an electrically actuated viscoelastic microbeam are investigated. For this purpose, a nonlinear finite element formulation of viscoelastic beams in combination with the fractional derivative constitutive equations is elucidated. The four-parameter fractional derivative model is used to describe the constitutive equations. The electric force acting on the microbeam is introduced and numerical methods for solving the nonlinear algebraic equation of quasi-static response and nonlinear equation of motion of dynamical response are described. The deflected configurations of a microbeam for different purely DC voltages and the tip displacement of the microbeam under a combined DC and AC voltages are presented. The validity of the present analysis is confirmed by comparing the results with those of the corresponding cases available in the literature.

• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.31-50
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• 2013

A five parameter viscoelastic model is developed to study harmonic waves propagating in the non-homogeneous viscoelastic filaments of varying density. The constitutive relation for five parameter model is first developed and then it is applied for harmonic waves in the specimen. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e., rod are space dependent. The specimen is non-homogeneous, initially unstressed and at rest. The method of non-linear partial differential equation has been used for finding the dispersion equation of harmonic waves in the rods. A simple method is presented for reflections at the free end of the finite non-homogeneous viscoelastic rods. The harmonic wave propagation in viscoelastic rod is also presented numerically with MATLAB.

• Proceedings of the Korean Fiber Society Conference
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• 1999.04a
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• pp.237-240
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• 1999

• Journal of KSNVE
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• v.10 no.1
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• pp.64-73
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• 2000

We present finite element equations in the Laplace-domain for linear viscoelastic and viscoelstically damped structures governed by a constitutive equation involving factional order derivative opeartors. These equations yield a nonstandard eigenproblem consisted of frequency dependent stiffness matrix. To solve this nonstandard eigenproblem we suggest an eigenvalue iteration procedure in the Laplace-domain. Improved Zenor and GHM material function type constitutive equations in the Laplace-domain are also available for this procedure. From above equations, complex eigenvalues and complex eigenvectors are obtained. Using obtained eigenvalues and eigenvectors, time domain analysis is performed by means of mode superposition. Finally, finite element solutions of viscoelastic and viscoeleastically damped sandwich beam are presented as an example.