• Title/Summary/Keyword: constitutive

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Numerical simulation of dimensional changes during sintering of tungsten carbides compacts

  • Bouvard, D.;Gillia, O.
    • Proceedings of the Korean Powder Metallurgy Institute Conference
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    • 1997.10a
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    • pp.7-7
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    • 1997
  • During sintering of very porous green bodies, as obtained by compaction of hard powders - such as tungsten carbide or ceramics - or by injection moulding, important shrinkage occurs. Due to heterogeneous green density field, gravity effects, friction on the support, thermal gradients, etc., this shrinkage is often non-uniform, which' may induce significant shape changes. As the ratio of compact dimension to powder size is very high, the mechanics of continuum is relevant to model such phenomena. Thus numerical techniques, such as the finite element method can be used to simulate the sintering process and predict the final shape of the sintered part. Such type of simulation has much been developed in the last decade firstly for hot isostatic pressing and next for die compaction. Finite element modelling has been recently applied to free sintering. The simulation of sintering should be based on constitutive equations describing the thermo-mechanical behaviour of the material under any state of stress and any temperature which may arise within the sintering body. These equations can be drawn either from experimental data or from micromechanical models. The experiments usually consist in free sintering and sinter-forging tests. Indeed applying more complex loading conditions at high temperature under controlled atmosphere is delicate. Micromechanical models describe the constitutive behaviour of aggregates of spheres from the deformation of two-sphere contact either by viscous flow or grain boundary diffusion. Such models are not able to describe complex microstructure and mechanisms as observed in real materials but they can give some basic information on the formulation of constitutive equations. Practically both experimental and theoretical approaches can be coupled to identify the constitutive equations. Such procedure has been performed for modelling the sintering of compacts obtained by die pressing of a mixture of tungsten carbide and cobalt powders. The constitutive behaviour of this material during sintering has been described by a linear viscous constitutive model, whose functions have been fitted from results of free sintering and sinter-forging experiments. This model has next been introduced in ABAQUS finite element code to simulate the sintering of heterogeneous green compacts of various geometries at constant temperature. Examples of simulations are shown and compared with experiments.

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Deep learning-based AI constitutive modeling for sandstone and mudstone under cyclic loading conditions

  • Luyuan Wu;Meng Li;Jianwei Zhang;Zifa Wang;Xiaohui Yang;Hanliang Bian
    • Geomechanics and Engineering
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    • v.37 no.1
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    • pp.49-64
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    • 2024
  • Rocks undergoing repeated loading and unloading over an extended period, such as due to earthquakes, human excavation, and blasting, may result in the gradual accumulation of stress and deformation within the rock mass, eventually reaching an unstable state. In this study, a CNN-CCM is proposed to address the mechanical behavior. The structure and hyperparameters of CNN-CCM include Conv2D layers × 5; Max pooling2D layers × 4; Dense layers × 4; learning rate=0.001; Epoch=50; Batch size=64; Dropout=0.5. Training and validation data for deep learning include 71 rock samples and 122,152 data points. The AI Rock Constitutive Model learned by CNN-CCM can predict strain values(ε1) using Mass (M), Axial stress (σ1), Density (ρ), Cyclic number (N), Confining pressure (σ3), and Young's modulus (E). Five evaluation indicators R2, MAPE, RMSE, MSE, and MAE yield respective values of 0.929, 16.44%, 0.954, 0.913, and 0.542, illustrating good predictive performance and generalization ability of model. Finally, interpreting the AI Rock Constitutive Model using the SHAP explaining method reveals that feature importance follows the order N > M > σ1 > E > ρ > σ3.Positive SHAP values indicate positive effects on predicting strain ε1 for N, M, σ1, and σ3, while negative SHAP values have negative effects. For E, a positive value has a negative effect on predicting strain ε1, consistent with the influence patterns of conventional physical rock constitutive equations. The present study offers a novel approach to the investigation of the mechanical constitutive model of rocks under cyclic loading and unloading conditions.

Generalization of Integration Methods for Complex Inelastic Constitutive Equations with State Variables (상태변수를 갖는 비탄성 구성식 적분법의 일반화)

  • Yun, Sam-Son;Lee, Sun-Bok;Kim, Jong-Beom;Lee, Hyeong-Yeon;Yu, Bong
    • 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.

Analysis of Thermo-Viscoplastic Behavior of Structures Using Unified Constitutive Equations (통일구성방정식을 이용한 구조물의 열점소성 거동에 관한 해석)

  • 윤성기;이주진
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.15 no.1
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    • pp.190-200
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    • 1991
  • Certain structural components are exposed to high temperatures. At high temperature, under thermal and mechanical loading, metal components exhibit both creep and plastic behavior. The unified constitutive theory is to model both the time-dependent behavior(creep) and the time-independent behavior(plasticity) in one set of equations. Microscopically both creep and plasticity are controlled by the motion of dislocations. A finite element method is presented encorporating a unified constitutive model for the transient analysis of viscoplastic behavior of structures exposed to high temperature.

Seismic Response Analysis at Multi-layered Ground During Large Earthquake (대형지진시 다층지반의 지진응답해석)

  • 김용성
    • Journal of the Korean Geotechnical Society
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    • v.18 no.4
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    • pp.55-64
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    • 2002
  • In the present study, in order to apply a cyclic viscoelastic-viscoplastic constitutive model to multi-layered ground conditions during large earthquake, the numerical simulations of the 1995 Hyogoken Nanbu Earthquake at Port Island, Kobe, Japan, were performed by the seismic response analysis. From the seismic response analysis, it was found that the acceleration calculated from the cyclic elasto-viscoplastic model and cyclic viscoelastic-viscoplastic models for clay was in close agreement with the recorded accelerations at the Port Island down-hole array, and the cyclic elastic-viscoplastic and viscoelastic-viscoplastic constitutive models showed little different behavior characteristics near clay layer. Thus, the propriety of viscoplastic model for clay was convinced. Therefore, it can be concluded that a cyclic viscoelastic-viscoplastic constitutive model can give a good description of the amplification and also it showed accurate damping characteristics of clay during large event which induces plastic deformation in large strain range.

Application of the EPU Constitutive Equation to expanded Polypropylene under Dynamic Loading (동하중을 받는 발포 폴리프로필렌에 대한 EPU 구성 방정식 적용)

  • Jeong, Kwang Young;Kim, Byeong-Jun;Cheon, Seong S.
    • Composites Research
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    • v.27 no.4
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    • pp.135-140
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    • 2014
  • A constitutive equation, which was suggested for describing the compressive deformation behaviour of the expanded polyurethane, was applied to the expanded polypropylene under dynamic loading. This equation consists of seven parameters, five of which are obtained by fitting the stress strain curve obtained from the quasi-static compression test at the lowest base strain rate. The remaining two parameters are able to be determined by fitting the curve from the compression test at different two stage strain rates. In order to check the eligibility of the equation at high strain rate, the impact test was performed and the results were compared to the analytical constitutive equation results for the expanded polypropylene with expansion ratios of 30 and 40 times, respectively.

Trap identification of the constitutive promoter-like sequences from the bacterial fish pathogen, as exemplified by Edwardsiella tarda

  • Lee, Sang-Yoon;Kim, Ki-Hong;Kim, Dong-Soo;Nam, Yoon-Kwon
    • Journal of fish pathology
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    • v.24 no.3
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    • pp.297-305
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    • 2011
  • A trap identification system for isolating functional sequences to allow the constitutive expression of foreign protein from Edwardsiella tarda was developed. Using the green fluorescent protein (GFP) reporter-based trap system, various functional sequences to drive heterologous expression of the GFP were selectable in Escherichia coli host. However from the bioinformatic sequence analysis, all the segments predicted as regulatory regions were not native promoters actually existing upstream of endogenous E. tarda genes. Instead, a number of non-authentic sequences, possibly resulted from the random shuffling and/or intermolecular ligation were also proven to be able to display a potent GFP expression in the recombinant E. coli. Further analysis with selected clones showed that both authentic and non-authentic sequences could function in as a constitutive promoter, leading quite a consistent and stable GFP expression after repetitive subcultures. Microscopic examination also confirmed the uniform pattern of GFP expression in every host bacterium. Semi-quantitative assay of GFP showed that there was no clear relationship between expression levels and organizational features of the promoters trapped. Functional promoter-like elements achieved in the present study could be a good starting material for multivalent genetic engineering of E. tarda in order to produce recombinant vaccines in a cost-effective fashion.

C]RASH ANALYSIS OF AUTO-BODY STRUCTURES CONSIDERING THE STRAIN-RATE HARDENING EFFECT

  • Kang, W.J.;Huh, H.
    • International Journal of Automotive Technology
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    • v.1 no.1
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    • pp.35-41
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    • 2000
  • The crashworthiness of vehicles with finite element methods depends on the geometry modeling and the material properties. The vehicle body structures are generally composed of various members such as frames, stamped panels and deep-drawn parts from sheet metals. In order to ensure the impact characteristics of auto-body structures, the dynamic behavior of sheet metals must be examined to provide the appropriate constitutive relation. In this paper, high strain-rate tensile tests have been carried out with a tension type split Hopkinson bar apparatus specially designed for sheet metals. Experimental results from both static and dynamic tests with the tension split Hopkinson bar apparatus are interpolated to construct the Johnson-Cook and a modified Johnson-Cook equation as the constitutive relation, that should be applied to simulation of the dynamic behavior of auto-body structures. Simulation of auto-body structures has been carried out with an elasto-plastic finite element method with explicit time integration. The stress integration scheme with the plastic predictor-elastic corrector method is adopted in order to accurately keep track of the stress-strain relation for the rate-dependent model accurately. The crashworthiness of the structure with quasi-static constitutive relation is compared to the one with the rate-dependent constitutive model. Numerical simulation has been carried out for frontal frames and a hood of an automobile. Deformed shapes and the Impact energy absorption of the structure are investigated with the variation of the strain rate.

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