• 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.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.275-282
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• 2017

The Fleck-Hutchinson theory on strain gradient plasticity (SGP), proposed in Adv. Appl Mech 33 (1997) 295, has recently been reformulated by adopting the strategy of decomposing the second order strain presented by Lam et al. in J Mech Pays Solids 51 (2003) 1477. The newly built SGP satisfies the non negativity of plastic dissipation, which is still an outstanding issue in other SGP theories. Furthermore, it explicitly shows how elastic strain gradients and corresponding elastic characteristic length scales come into play in general elastic-plastic loading histories. In this study, the relation between elastic length scales and plastic length scales is investigated by taking wire torsion as an example. It is concluded that the size effects arising when two sets of length scales are of the same order are essentially elastic instead of plastic.

• Geomechanics and Engineering
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• v.8 no.1
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• pp.33-52
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• 2015

Based on the Mohr-Coulomb failure criterion, a gradient-dependent plastic model that considers the strain-softening behavior is presented in this study. Both triaxial shear tests on conventional specimen and precut-specimen, which were obtained from an ancient landslide, are performed to plot the post-peak stress-strain entire-process curves. According to the test results of the soil strength, which reduces from peak to residual strength, the Mohr-Coulomb criterion that considers strain-softening under gradient plastic theory is deduced, where strength reduction depends on the hardening parameter and the Laplacian thereof. The validity of the model is evaluated by the simulation of the results of triaxial shear test, and the computed and measured curves are consistent and independent of the adopted mesh. Finally, a progressive failure of the ancient landslide, which was triggered by slide of the toe, is simulated using this model, and the effects of the strain-softening process on the landslide stability are discussed.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.3
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• pp.94-102
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• 1996

An interpretation for the additive and multiplicative decomposition theory of the deformation gradient tensor in finite deformation problems is presented. the conventional methods have not provided the additive deformation velocity gradient. Moreover the plastic deformation velocity gradients are not free from elastic deformations. In this paper, a modified multiplicative decomposition is introduced with the assumption of coaxial plastic deformation velocity gradient. This strategy well gives the additive deformation velocity gradient in which the plastic deformation velocity gradient is not affect4d by the elastic deformation.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.528-535
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• 2011

In the present, the formation of shear band under a simple shear deformation is investigated using a rate-independent elastic-plastic constitutive relations. Moreover, the strain gradient terms are incorporated to obtain a non-local plastic constitutive relation, which in turn represented using combined two-back stress hardening model. Then, the continuum damage model is also included to the proposed model. The post-localization behavior are studied by introducing a small imperfection in a work piece. The strain gradient affects the shear localization significantly such that the intensity of shear band decreases as the strain gradient coefficient increases when the J2 flow theory is employed.

• 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.

• 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.

• Journal of Welding and Joining
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• v.17 no.2
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• pp.91-96
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• 1999

The problems of welding distortion in a welded structures are major concern in heavy industry. Weld-induced angular distortion's formula, composed weld parameter such as heat input and plate thickness, is developed analytically by the use of an elliptic cylindrical inclusion with an eigenstrain in an infinite laminated plate theory. The source of angular distortion in weldments is the plastic strains, which are caused by non-uniform temperature gradient. The distributions of the plastic strain corresponding eigenstrain are assumed by the use of Rosenthal's solution expressing thermal history. Comparison of calculated results with experimental data shows the accuracy and validity of the proposed method.

• Journal of Mechanical Science and Technology
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• v.20 no.5
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• pp.621-633
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• 2006

To reflect the size effect of material $(1\sim15{\mu}m)$ during plastic deformation of polycrystalline copper, a constitutive equation which includes the strain gradient plasticity theory and intrinsic material length model is coupled with the finite element analysis and applied to plane strain deformation problem. The method of least square has been used to calculate the strain gradient at each element during deformation and the effect of distributed force on the strain gradient is investigated as well. It shows when material size is less than the intrinsic material length $(1.54{\mu}m)$, its deformation behavior is quite different compared with that computed from the conventional plasticity. The generation of strain gradient is greatly suppressed, but it appears again as the material size increases. Results also reveal that the strain gradient leads to deformation hardening. The distributed force plays a role to amplify the strain gradient distribution.

• Journal of Korean Society on Water Environment
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• v.29 no.5
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• pp.691-702
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• 2013

This review paper summarizes the theory, application, and potential drawbacks of diffusive gradient in thin film (DGT) probe which is a widely used in-situ passive sampling technique for monitoring inorganic contaminants in aquatic environments. The DGT probe employs a series of layers including a filter membrane, a diffusive hydrogel, and an ionic exchange resin gel in a plastic unit. The filter side is exposed to an aquatic environment after which dissolved inorganic contaminants, such as heavy metals and nuclides, diffuse through the hydrogel and are accumulated in the resin gel. After retrieval, the contaminants in the resin gel are extracted by strong acid or base and the concentrations are determined by analytical instruments. Then aqueous concentrations of the inorganic contaminants can be estimated from a mathematical equation. The DGT has also been used to monitor nutrients, such as ${PO_4}^{3-}$, in lakes, streams, and estuaries, which might be helpful in assessing eutrophic potential in aquatic environments. DGT is a robust in-situ passive sampling techniques for investigating bioavailability, toxicity, and speciation of inorganic contaminants in aquatic environments, and can be an effective monitoring tool for risk assessment.