• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.311-326
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• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.829-850
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• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• Land and Housing Review
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• v.11 no.2
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• pp.95-104
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• 2020

This study aims to explore a purely mechanistic pavement analysis approach where viscoelasticity and fracture of asphalt mixtures are considered to accurately predict deformation and damage behavior of flexible pavements. To do so, the viscoelastic and fracture properties of designated pavement materials are obtained through experiments and a fully mechanistic damage analysis is carried out using a finite element method (FEM). While modeling crack development can be done in various ways, this study uses the cohesive zone approach, which is a well-known fracture mechanics approach to efficiently model crack initiation and propagation. Different pavement configurations and traffic loads are considered based on three main functional classes of roads suggested by FHWA i.e., arterial, collector and local. For each road type, three different material combinations for asphalt concrete (AC) and base layers are considered to study damage behavior of pavement. A concept of the approach is presented and a case study where three different material combinations for AC and base layers are considered is exemplified to investigate progressive damage behavior of pavements when mixture properties and layer configurations were altered. Overall, it can be concluded that mechanistic pavement modeling attempted in this study could differentiate the performance of pavement sections due to varying design inputs. The promising results, although limited yet to be considered a fully practical method, infer that a few mixture tests can be integrated with the finite element modeling of the mixture tests and subsequent structural modeling of pavements to better design mixtures and pavements in a purely mechanistic manner.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2148-2158
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• 1996

Uncoupled, quasi-static and linear thermoviscoelastic problems are analyzed in time domain by the finite element approximation which is developed using the principle of virtual work and viscoelasticity matrices instead of shear and bulk relaxation functions as in usual formulations. The material is assumed to be isotropic, homegeneous and thermorheologically simple, which means that the temperature-time equivalence postulate is effective. The stress-strain laws are expressed by relaxation-type hereditary integrals. In spatial and time discritizations, isoparametric quadratic quadrilateral finite elements and linear time variations are adopted. For explicit derivations, the viscoelastic material is assumed to behave standard linear solid in shear and elastically in dilatation. Two-dimensional examples are solved under general temperature distributions T = T(x, t), and compared with other opproximate solutions to show the versatility of the presented analysis.

• Structural Engineering and Mechanics
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• v.40 no.6
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• pp.783-800
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• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1429-1437
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• 1992

A new finite element formulation based on the relaxation type hereditary integral is presented for a time-domain analysis of isotropic, linear viscoelastic problems. The semi-discrete variational approximation and elastic-viscoelastic correspondence principle are used in the theoretical development of the proposed method. In a time-stepping procedure of final, linear algebraic system equations, only a small additional computation for past history is required since the equivalent stiffness matrix is constant. The viscoelasticity matrices are derived and the stress computation algorithm is given in matrix form. The effect of time increment and Gauss point numbers on the numerical accuracy is examined. Two dimensional numerical examples of plane strain and plane stress are solved and compared with the analytical solutions to demonstrate the versatility and accuracy of the present method.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.23 no.5
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• pp.358-363
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• 2010

The polishing pad is important element for polishing characteristic such as material removal rate(MRR) and within wafer non-uniformity(WIWNU) in the chemical mechanical planarization(CMP). The result of the viscoelasticity measurement shows that 1st elastic modulus is increased and 2nd elastic modulus is decreased when the top pad is thickened. The finite element analysis(FEA) was conducted to predict characteristic of polishing behavior according to the pad thickness. The result of polishing experiment was similar with the FEA, and it shows that the 1st elastic modulus affects instantaneous deformation of pad related to MRR. And the 2nd elastic modulus has an effect on WIWNU due to the viscoelasticity deformation of pad.

• Structural Engineering and Mechanics
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• v.1 no.1
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• pp.103-118
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• 1993

The near field is discretized into finite elements, and the far field into infinite elements. Closed form far-field solutions to three fundamental problems are used as the shape functions of the infinite elements. Such infinite elements are capable of transmitting all surface and body waves. An efficient scheme to integrate numerically the stiffness and mass matrices of these elements in presented. Results agree closely with those obtained by others.

• Transactions of Materials Processing
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• v.13 no.2
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• pp.180-187
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• 2004

A computer code was developed to simulate the filling stage of the injection/compression molding process by a finite element method. The constitutive equation used here was the compressible Leonov model. The PVT relationship was assumed to follow the Tait equation. The flow-induced birefringence was related to the calculated flow stresses through the linear stress-optical law. Simulations of a disk part under different process conditions including the variation of compression stroke and compression speed were carried out to understand their effects on birefringence variation. The simulated results were also compared with those by conventional injection molding.

• Composites Research
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• v.27 no.4
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• pp.174-181
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• 2014

This study describes viscoelasticity analysis of carbon-fiber reinforced polymer matrix composite material. One of the most important problem during high temperature molding process is residual stress. Residual stress can cause warpage and cracks which can lead to serious defects of the final product. For the difference in thermal expansion coefficient and change of resin property during curing, it is difficult to predict the final deformed shape of carbon-fiber reinforced polymer matrix composite. The consideration of chemical shrinkage can reduce the prediction errors. For this reason, this study includes the viscoelasticity and chemical shrinkage effects in FE analysis by creating subroutines in ABAQUS. Analysis results are compared with other researches to verify the validity of the subroutine developed, and several stacking sequences are introduced to compare tested results.