• Multiscale and Multiphysics Mechanics
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• v.1 no.2
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• pp.171-188
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• 2016

Gradient enhanced theories of crystal plasticity enjoy great research interest. The focus of this work is on thermodynamically consistent modeling of grain size dependent hardening effects. In this contribution, we develop a model framework for damage coupled to gradient enhanced crystal thermoplasticity. The damage initiation is directly linked to the accumulated plastic slip. The theoretical setting is that of finite strains. Numerical results on single-crystalline metal showing the development of damage conclude the paper.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.87-97
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• 2004

In gradient-dependent plasticity theory, the yield strength depends on the Laplacian of an equivalent plastic strain measure (hardening parameter), and the consistency condition results in a differential equation with respect to the plastic multiplier. The plastic multiplier is then discretized in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The disadvantage is that the plastic multiplier requires a Hermitian interpolation that has four degrees of freedom at each node. Instead of using a Hermitian interpolation, in this article, a 3-node incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but it is continuous across element boundaries and its second-order derivatives exist within the elements. It greatly reduces the degrees of freedom for a problem, and is shown through a numerical example on localization to yield good results.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.413-417
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• 2004

Recent experiments have shown the 'size effects' in micro/nano scale. But the classical plasticity theories can not predict these size dependent deformation behaviors because their constitutive models have no characteristic material length scale. The Mechanism - based Strain Gradient(MSG) plasticity is proposed to analyze the non-uniform deformation behavior in micro/nano scale. The MSG plasticity is a multi-scale analysis connecting macro-scale deformation of the Statistically Stored Dislocation(SSD) and Geometrically Necessary Dislocation(GND) to the meso-scale deformation using the strain gradient. In this research we present a study of nano-indentation by the MSG plasticity. Using W. D. Nix and H. Gao s model, the analytic solution(including depth dependence of hardness) is obtained for the nano indentation , and furthermore it validated by the experiments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.914-922
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• 2003

In this paper, the strain localization of voided ductile material has been analyzed by nonlocal plasticity formulation in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The gradient terms in yield criterion show an important role on modeling strain-softening phenomena of material. The influence of the mesh size on the elastic -plastic deformation behavior and the effect of the characteristic length parameter for localization prediction are also investigated. The proposed nonlocal plasticity shows that the load -strain curves converge to one curve. Results using nonlocal plasticity also exhibit the dependence of mesh size is much less sensitivity than that for a corresponding local plasticity formulation.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.223-232
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• 2019

Since the actuators with small- scale structures may be exposed to external reciprocal actions lead to create undesirable loads causing instability, the buckling behaviors of them are interested to make reliable or accurate actions. Therefore, the purpose of this paper is to analyze plastic buckling behavior of the micro beam structures by adopting a Conventional Mechanism-based Strain Gradient plasticity (CMSG) theory. The effect of length scale on critical force is considered for three types of boundary conditions, i.e. the simply supported, cantilever and clamped - simply supported micro beams. For each case, the stability equations of the buckling are calculated to obtain related critical forces. The constitutive equation involves work hardening phenomenon through defining an index of multiple plastic hardening exponent. In addition, the Euler-Bernoulli hypothesis is used for kinematic of deflection. Corresponding to each length scale and index of the plastic work hardening, the critical forces are determined to compare them together.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.9
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• pp.1041-1050
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• 2011

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.10a
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• pp.109-112
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• 2000

This paper presents an analytical study that can predict the path-dependent forming limits for bilinear strain paths. To predict the forming limit diagrams(FLD), the analytical procedure was performed within the framework of Marciniak and Kuczynski approach by introducing the effect of the existence of strain gradient over the stretching punch. The predicted path-dependent forming limits of an anisotropic sheet were compared with the published experimental results. It was found that the predicted path-dependent forming limits were in good agreement with the experimental data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.7
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• pp.745-751
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• 2011

This study proposes finite element modeling of dislocation punching at cooling after consolidation in order to calculate the strength of particle-reinforced aluminum composites. The Taylor dislocation model combined with strain gradient plasticity around the reinforced particle is adopted to take into account the size-dependency of different volume fractions of the particle. The strain gradients were obtained from the equivalent plastic strain calculated during the cooling of the spherical unit cell, when the dislocation punching due to CTE (Coefficient of Thermal Expansion) mismatch is activated. The enhanced yield stress was observed by including the strain gradients, in an average sense, over the punched zone. The tensile strength of the SiCp/Al 356-T6 composite was predicted through the finite element analysis of an axisymmetric unit cell for various sizes and volume fractions of the particle. The predicted strengths were found to be in good agreement with the experimental data. Further, the particle-size dependency was clearly established.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.05a
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• pp.205-208
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• 2001

Localized shear band is investigated through the analysis of one-dimensional model for simple shearing deformation of thermally rate dependent material. Generally mesh size or interval of nodes play an important role in determining the overall flow behavior of the material. In order to observe these size effects we adapted non-local theory by including higher order strain gradients of the equivalent strain into the constitutive equation for the flow stress. for the ease of convergence and numerical stability the inplicit finite difference scheme is employed.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.237-255
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• 2013

In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.