• 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.

• Structural Engineering and Mechanics
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• v.22 no.1
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• pp.107-130
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• 2006

The paper deals with the numerical solution of the dynamic problem of masonry structures. Masonry is modelled as a non-linear elastic material with zero tensile strength and infinite compressive strength. Due to the non-linearity of the adopted constitutive equation, the equations of the motion must be integrated directly. In particular, we apply the Newmark or the Hilber-Hughes-Taylor methods implemented in code NOSA to perform the time integration of the system of ordinary differential equations obtained from discretising the structure into finite elements. Moreover, with the aim of evaluating the effectiveness of these two methods, some dynamic problems, whose explicit solutions are known, have been solved numerically. Comparisons between the exact solutions and the corresponding approximate solutions obtained via the Newmark and Hilber-Hughes-Taylor methods show that in the cases under consideration both numerical methods yield satisfactory results.

• Proceedings of the KSR Conference
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• 2009.05a
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• pp.1592-1597
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• 2009

Ratcheting is a cyclic accumulation of strain under a cyclic loading. It is a kind of mechanisms which generate cracks in rail steels. Though some experimental and numerical study has been performed, modeling of ratcheting is still a challenging problem. In this study, an elastic-plastic constitutive equation considering non-linear kinematic hardening and isotropic hardening was applied. Under the tangential stress of the contact stresses, a cyclic stress-strain relation was obtained by using the model. Strain under repeated cycles was accumulated.

• Transactions of Materials Processing
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• v.17 no.1
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• pp.19-26
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• 2008

In the present work, the ratcheting behavior under uniaxial cyclic loading is analyzed. A comparison between the published and the results from the present model is also included. In order to simulate the ratcheting behavior, Two-Back Stress model is proposed by combining the non-linear Armstrong-Frederick rule and the non-linear Phillips hardening rule based on kinematic hardening equation. It is shown that some ratcheting behaviors can be obtained by adjusting the control material parameters and various evolutions of the kinematic hardening parameter can be obtained by means of simple combination of hardening rules using simple rule of mixtures. The ultimate back stress is also derived for the present combined kinematic hardening models.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1075-1083
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• 2000

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Journal of the Korean Society for Railway
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• v.11 no.3
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• pp.311-316
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• 2008

Ratcheting is a cyclic accumulation of strain under a cyclic loading. It is a kind of mechanisms which generate cracks in rail steels. Though some experimental and numerical study has been performed, modeling of ratcheting is still a challenging problem. In this study, an elastic-plastic constitutive equation with non-linear kinematic hardening equation was applied. Contact stresses in wheel-rail were analyzed. Under the tangential stress of the contact stresses, a cyclic stress-strain relation was obtained by using the model. A constant ratcheting strain per cycle was accumulated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.2113-2122
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• 1994

The 3-D FEM analysis for simulating the stamping operation of planar anisotropic sheet metals with arbitrarily-shaped tools is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relations, comprising equilibrium equation and mesh-normal geometric constraints, is appropriately linearized. The linear triangular elements are used for depicting the formed sheet, based on membrane approximation. Barlat's non-quadratic anisotropic yield criterion(strain-rate potential) is employed, whose in-plane anisotropic properties are taken into account with anisotropic coefficients and non-quadratic function parameter. The planar anisotropic finite element formulation is tested with the numerical simulations of the stamping of an automotive hood inner panel and the drawing of a hemispherical punch. The in-plane anisotropic effects on the formability of both mild steel and aluminum alloy sheet metals are examined.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1562-1570
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• 2003

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. The radial return mapping is one of the most robust integration scheme currently used. Nonlinear kinematic hardening model of Armstrong-Fredrick type has recovery term and the direction of kinematic hardening increment is not parallel to that of plastic strain increment. In this case, The conventional radial return mapping method cannot be applied directly. In this investigation, we expanded the radial return mapping method to consider the nonlinear kinematic hardening model and implemented this integration scheme into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using Newton method and bisection method. Using dynamic yield condition derived from linearization of flow rule, the integration scheme for elastoplastic and viscoplastic constitutive model was unified. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Advances in nano research
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• v.9 no.3
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• pp.157-172
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• 2020

The aim of this present research is the effect of the higher-order terms of the governing equation on the forced longitudinal vibration of a nanorod model and making comparisons of the results with classical nonlocal elasticity theory. For this purpose, the free axial vibration along with forced one under the two various linear and harmonic axial concentrated forces in zigzag Single-Walled Carbon Nanotube (SWCNT) are analyzed dynamically. Three various theories containing the classical theory, which is called Eringen's nonlocal elasticity, along with Rayleigh and Bishop theories (higher-order theories) are established to justify the nonlocal behavior of constitutive relations. The governing equation and the related boundary conditions are derived from Hamilton's principle. The assumed modes method is adopted to solve the equation of motion. For the free axial vibration, the natural frequencies are calculated for the various values of the nonlocal parameter only based on Eringen's theory. The effects of the nonlocal parameter, thickness, length, and ratio of the excitation frequency to the natural frequency over time in dimensional and non-dimensional axial displacements are investigated for the first time.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.518-522
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• 2008

Recently, many patients related to heart disease have surgical operation by expanding a blood vessel to treat the angiostenosis. So far most angioplasties have been performed using balloon-dilative stent made of stainless steel. Some researchers are studying the stent made of shape memory alloy (SMA) to operate the angioplasty more easily. and there are several papers which introduce the angioplasty using SMA. However, most of the analysis models for stents are constructed using solid elements. So much computing time is required to solve the analysis model. In this study, we suggest the SMA stent model using 1D truss element which is much faster than stent model using 3D solid element. To represent non-linear behavior of SMA, we apply 1D SMA constitutive equation of Lagoudas'. Pseudo-elastic behavior of stent structures is presented as a numerical example.