• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.69-75
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• 1995

The deformation behavior of stainless steel-clad aluminum sheet metals under uniaxial tension has been investigated. The differences in mechanical properties such as elastic modulus, flow stress and plastic strain ratio, of component layers of the composite sheet gave rise to warping of the tensile specimens. The warping has been analyzed by FEM and the total force and momentum equilibria. The analyzed radii of curvature of the warped specimens were smaller than the measured data possibly due to elastic recovery during unloading. The differences in mechanical properties may also give rise to transverse stresses in the component layers. The transverse stresses have been analyzed on the assumption of isostrain and by the FEM in which the warping has been taken into account. The transverse stresses calculated by the FEM were lower than those by the isostrain hypothesis due to stress relaxation by the warping and turned out to be negligible compared with the longitudinal stresses. Consequently, the flow stresses of the composite sheets follow the rule of mixtures.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.169-178
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• 1991

A plane-strain finite element analysis of sheet metal forming is carried out by using the rigid-plastic FEM based on the membrane theory. The sheet material is assumed to possess normal anisotropy and to obey Hill's new yield criterion and its associated flow rule. A formulation of initial guess generation for the displacement field is derived by using the nonlinear elastic FEM. A method of contact treatment is proposed in which the skew boundary condition for arbitrarily shaped tools is successively used during iteration. In order to verify the validity of the developed method, plane-strain drawing with tools in analytic expression and with arbitrarily shaped tools is analyzed and compared with the published results. The comparison shows that the present method can be effectively used in the analysis of plane-strain sheet metal forming and thus provides the basis of approximate sectional analysis of panel-like sheet forming.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.11-23
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• 2020

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.619-626
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• 2018

A simple prediction procedure was investigated for calculating the stresses and displacements of a circular opening. Unlike existed approaches, the proposed approach starts each step with a radius increment. The stress for each annulus could be obtained analytically, while strain increments for each step can be determinate numerically from the compatility equation by finite difference approximation, flow rule and Hooke's law. In the successive manner, the distributions of stresses and displacements could be found. It should be noted that the finial radial stress and displacement were equal to the internal supporting pressure and deformation at the tunnel wall, respectively. By assuming different plastic radii, GRC and the evolution curve of plastic radii and internal supporting pressures could be obtained conveniently. Then the real plastic radius can be calculated by using linear interpolation in the evolution curve. Some numerical and engineering examples were performed to demonstrate the accuracy and validity for the proposed procedure. The comparisons results show that the proposed procedure was faster than that in Lee and Pietrucszczak (2008). The influence of annulus number and dilation on the accuracy of solutions was also investigated. Results show that the larger the annulus number was, the more accurate the solutions were. Solutions in Park et al. (2008) were significantly influenced by dilation.

• 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.

• Journal of the Korean Geotechnical Society
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• v.30 no.1
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• pp.49-63
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• 2014

Bearing capacity factor $N_{\gamma}$ and shape factor were studied for rigid strip and circular footings with a rough base on sand by numerical modelling considering the effect of dilation angle. The numerical model was developed with an explicit finite difference code. Loading procedures and interpretation methods were devised in order to shorten the running time while eliminating the exaggeration of the reaction caused by the explicit scheme. Using the Mohr-Coulomb plasticity model with associated (${\psi}={\phi}$) and nonassociated (${\psi}$ < ${\phi}$) flow-rules, the bearing capacity factor $N_{\gamma}$ was evaluated for various combinations of internal friction angles and dilation angles. Bearing capacity factor decreased as the dilation angle was reduced from the associated condition. An equation applicable to typical sands was proposed to evaluate the relative bearing capacity for the nonassociated condition compared to the associated condition on which most bearing capacity factor equations are based. The shape factor for the circular footing varied substantially when the plane-strain effect was taken into account for the strip footing. The numerical results of this study showed closer trends with the previous experimental results when the internal friction angle was increased for the strip footing. Discussions are made on the reason that previous equations for the shape factor give different results and recommendations are made for the appropriate design shape factor.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.1015-1038
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• 2016

In the current research an advanced criterion with non-associated flow rule (non-AFR) for depicting the behavior of anisotropic sheet metals is presented to consider the strength differential effects (SDEs) for these materials. Owing to the fact that Lou et al. (2013) yield function is dependent on structure of an anisotropic material (BCC, FCC and HCP), an advanced yield function with inspiring of Yoon et al. (2014) yield function is proposed which is dependent upon anisotropic structures. Furthermore, to compute Lankford coefficients, a new pressure sensitive plastic potential function which would be dependent to anisotropic structure is presented and coupled with the proposed yield function with employing a non-AFR in a novel criterion which is called here 'dvanced criterion'. Totally eighteen experimental data are required to calibrate the criterion contained of directional tensile and compressive yield stresses for the yield function and directional Lankford coefficients for the plastic potential function. To verify the criterion, three anisotropic sheet metals with different structures are taken as case studies such as Al 2008-T4 (a BCC material), Al 2090-T3 (a FCC material) and AZ31 (a HCP material).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2019-2031
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• 2004

The least-squares formulation for rigid-plasticity based on J$_2$-flow rule and infinitesimal theory and its meshfree implementation using moving least-squares approximation are proposed. In the least-squares formulation the squared residuals of the constitutive and equilibrium equations are minimized. Those residuals are represented in a form of first-order differential system using the velocity and stress components as independent variables. For the enforcement of the boundary and frictional contact conditions, penalty scheme is employed. Also the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near the contact interface. The proposed least-squares meshfree method does not require any structure of extrinsic cells during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.71-78
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• 1997

The high precision analysis by the p-version of the finite element method are fairly well established as highly efficient method for linear elastic problems, especially in the presence of stress singularity. It has been noted that the merits of p-version are accuracy, modeling simplicity, robustness, and savings in user's and CPU time. However, little has been done to exploit their benefits in elasto-plastic analysis. In this paper, the p-version finite element model is proposed for the materially nonlinear analysis that is based on the incremental theory of plasticity, the associated flow rule, and von-Mises yield criteria. To obtain the solution of nonlinear equation, the Newton-Raphson method and initial stiffness method, etc are used. Several numerical examples are tested with the help of the square plates with cutout, the thick-walled cylinder under internal pressure, and the center cracked plate under tensile loading. Those results are compared with the there cal solutions and the numerical solutions of ADINA software.

• Geomechanics and Engineering
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• v.17 no.4
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• pp.405-411
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• 2019

A significant influence of the particle size distribution on the resilient behaviour of granular aggregates was usually observed in laboratory tests. However, the mechanisms underlying this phenomenon were rarely reached. In this study, a mechanistic model considering particle breakage is proposed. It is found to be the combined effects of the coefficient of uniformity and the size range between maximum and minimum particle sizes that influences the resilient modulus of granular aggregates. The resilient modulus is found to undergo reduction with evolution of particle breakage by shifting the initial particle size distribution to a broader one.