• International Journal of Aeronautical and Space Sciences
• /
• v.13 no.4
• /
• pp.458-467
• /
• 2012

In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

• Transactions of Materials Processing
• /
• v.18 no.1
• /
• pp.20-25
• /
• 2009

A finite element analysis was carried out for a 4:1 planar contraction die for polymer melts using the viscoelastic constitutive equation of Leonov. Viscoelastic fluids showed significant differences in pressure drop and birefringence in contraction and expansion flows. The pressure drop was higher and the birefringence smaller in expansion than in contraction flow. The difference increased with increasing flow rate. The nonlinear Leonov model was shown to describe the viscoelastic effects observed in experiments.

• Proceedings of the Korean Society of Rheology Conference
• /
• 2000.11a
• /
• pp.3-6
• /
• 2000

• Proceedings of the Korean Society of Rheology Conference
• /
• 2001.06a
• /
• pp.25-28
• /
• 2001

• Journal of Mechanical Science and Technology
• /
• v.14 no.1
• /
• pp.19-29
• /
• 2000

A viscoelastic finite element analysis is presented to investigate residual stresses occurred in a laminated cylindrical shell during cure. An incremental viscoelastic constitutive equation that can describe stress relaxation during the cure is derived as a recursive formula which can be used conveniently for a numerical analysis. The finite element analysis program is developed on the basis of a 3-D degenerated shell element and the first order shear deformation theory, and is verified by comparing with an one dimensional exact solution. Viscoelastic effect on the residual stresses in the laminated shell during the cure is investigated by performing both the viscoelastic and linear elastic analyses considering thermal deformation and chemical shrinkage simultaneously. The results show that there is big difference between viscoelastic stresses and linear elastic stresses. The effect of cooling rates and cooling paths on the residual stresses is also examined.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.05a
• /
• pp.289-294
• /
• 2001

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear phenomena.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.1
• /
• pp.57-64
• /
• 2002

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytical solutions of the system. The frequency-response curves sallow that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear Phenomena.

• Korea-Australia Rheology Journal
• /
• v.16 no.4
• /
• pp.183-191
• /
• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1672-1677
• /
• 2003

In this paper, the spectral element model is derived for the vibration and stability analyses of an axially moving viscoelastic beam subjected to axial tension. The viscoelastic material is represented by using a one-dimensional constitutive equation of hereditary integral type. The accuracy of the present spectral element model is first verified by comparing the eigenvalues obtained by the present spectral element model-based SEM with those obtained by the exact theory and the conventional FEM. The effects of viscoelasticity on the vibration and stability of an example moving viscoelastic beam are numerically investigated.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.4D
• /
• pp.387-393
• /
• 2010

This paper studies static crack growth of asphalt pavement using the extended finite element method (XFEM). To consider nonlinear characteristics of asphalt concrete, a viscoelastic constitutive equation using the Maxwell chain is used. And a linear cohesive crack model is used to regularize the crack. Instead of constructing the viscoelastic constitutive law from the Prony approximation of compliance and retardation time measured experimentally, we use a smooth log-power function which optimally fits experimental data and is infinitely differentiable. The partial moduli of the Maxwell chain from the log-power function make analysis easy because they change more smoothly in a more stable way than the ordinary method such as the least square method. Using the developed method, we can simulates the static crack growth test results satisfactorily.