• Title/Summary/Keyword: Constitutive Relation

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Nonlinear Finite Element Analysis of RC Shear Walls under Cyclic Loadings (반복하중을 받는 철근콘크리트 전단벽의 비선형 유한요소 해석)

  • 곽효경;김도연
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.4
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    • pp.353-367
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    • 2003
  • This paper describes the extension of the numerical model, which was developed to simulate the nonlinear behavior of reinforced concrete (RC) structures subjected to monotonic in plane shear and introduced in the companion paper, to simulate effectively the behavior of RE structures under cyclic loadings. While maintaining all the basic assumptions adopted in defining the constitutive relations of concrete under monotonic loadings, a hysteretic stress strain relation of concrete, which across the tension compression region, is defined. In addition, unlike previous simplified stress strain relations, curved unloading and reloading branches inferred from the stress strain relation of steel considering the Bauschinger effect we used. The modifications of the stress strain relation of steel are also introduced to reflect pinching effect depending on the shear span ratio and an average stress distribution in a cracked RC element. Finally, correlation studies between analytical results and experimental studies are conducted to establish the validity of the proposed model.

Nonexistence and non-decoupling of the dissipative potential for geo-materials

  • Liu, Yuanxue;Zhang, Yu;Wu, Runze;Zhou, Jiawu;Zheng, Yingren
    • Geomechanics and Engineering
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    • v.9 no.4
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    • pp.531-545
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    • 2015
  • Two fundamental issues exist in the damage theory of geo-material based on the concept of thermodynamics: existence or nonexistence of the dissipation potential, and whether the dissipation potential could be decoupled into a damage potential and a plastic one or not. Thermodynamics theory of elastoplastic damage assumes the existence of dissipation potential, but the presence of dissipation potential is conditional. Based on the dissipation inequality in accord with the second law of thermodynamics, the sufficient and necessary conditions are given for the existence of the dissipation potential separately in total and incremental forms firstly, and proved strictly in theory. With taking advantage of the basic mechanical properties of geo-materials, the nonexistence of the dissipative potential is verified. The sufficient and necessary conditions are also given and proved for the decoupling of the dissipation potential of geo-materials in total and incremental forms. Similarly, the non-decoupling of the dissipation potential has also been proved, which indicates the dissipation potential of geo-materials in total or incremental forms could not be decoupled into a dissipative potential for plasticity and that for damage respectively. The research results for the fundamental issues in the thermodynamics theory of damage will help establish and improve the theoretic basis of elastoplastic damage constitutive model for geo-materials.

The Analysis of Soil Behaviour by Double Surface Work-hardening Constitutive Model (복합항복면 일-경화구성 모델을 이용한 지반거동해석)

  • Youn, Il-Ro;Oh, Se-Wook
    • Journal of the Korean Society of Industry Convergence
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    • v.15 no.1
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    • pp.21-27
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    • 2012
  • Decomposed granite soils are in a wide range of conditions depending on the degrees of weathering. This paper is intended to examine laboratory tests such as consolidation tests and conventional triaxial compression tests conducted in order to find out the mechanical properties of Cheongju granite soil. Along with the foregoing, the results of basic physical tests conducted in order to grasp the physical properties of Cheongju granite soil were described and based on the results, methods to calculate the mechanical parameters of numerical approaches using Lade's double surface work-hardening constitutive model were examined. Finally, it is intended to explain the stress properties of Cheongju granite soil used as a geotechnical material based on its shear behavior and critical state concept using the results of isotropic consolidation tests and triaxial compression tests. As a conclusion, it can be seen that in the relationship between confining stress and maximum deviator stress, the slope is maintained at a constant value of 2.95. In the drained CTC test, maximum deviator stress generally existed in a range of axial strain of 6~8% and larger dilatancy phenomena appeared when confining stress was smaller. Finally, based on the results of the CTC tests on Cheongju granite soil, although axial strain, deviator stress and pore water pressure showed mechanical properties similar to those of overconsolidated soil, Cheongju granite soil showed behavior similar to that of normally consolidated soil in terms of volumetric strain.

Nonexistence and non-decoupling of the dissipative potential for geo-materials

  • Liu, Yuanxue;Zhang, Yu;Wu, Runze;Zhou, Jiawu;Zheng, Yingren
    • Geomechanics and Engineering
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    • v.9 no.5
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    • pp.569-583
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    • 2015
  • Two fundamental issues exist in the damage theory of geo-material based on the concept of thermodynamics: existence or nonexistence of the dissipation potential, and whether the dissipation potential could be decoupled into a damage potential and a plastic one or not. Thermodynamics theory of elastoplastic damage assumes the existence of dissipation potential, but the presence of dissipation potential is conditional. Based on the dissipation inequality in accord with the second law of thermodynamics, the sufficient and necessary conditions are given for the existence of the dissipation potential separately in total and incremental forms firstly, and proved strictly in theory. With taking advantage of the basic mechanical properties of geo-materials, the nonexistence of the dissipative potential is verified. The sufficient and necessary conditions are also given and proved for the decoupling of the dissipation potential of geo-materials in total and incremental forms. Similarly, the non-decoupling of the dissipation potential has also been proved, which indicates the dissipation potential of geo-materials in total or incremental forms could not be decoupled into a dissipative potential for plasticity and that for damage respectively. The research results for the fundamental issues in the thermodynamics theory of damage will help establish and improve the theoretic basis of elastoplastic damage constitutive model for geo-materials.

Nonlinear large deflection buckling analysis of compression rod with different moduli

  • Yao, Wenjuan;Ma, Jianwei;Gao, Jinling;Qiu, Yuanzhong
    • Structural Engineering and Mechanics
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    • v.54 no.5
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    • pp.855-875
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    • 2015
  • Many novel materials exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, firstly, the nondimensional expression of the relation between offset of neutral axis and deflection curve is derived based on the phased integration method, and then using the energy method, load-deflection relation of the rod is determined; Secondly, based on the improved constitutive model for different moduli, large deformation finite element formulations are developed and combined with the arc-length method, finite element iterative program for rods with different moduli is established to obtain buckling critical loads; Thirdly, material mechanical properties tests of graphite, which is the raw material of graphene, are performed to measure the tensile and compressive elastic moduli, moreover, buckling tests are also conducted to investigate the buckling behavior of this kind of graphite rod. By comparing the calculation results of the energy method and finite element method with those of laboratory tests, the analytical model and finite element numerical model are demonstrated to be accurate and reliable. The results show that it may lead to unsafe results if the classic theory was still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed models could provide a novel approach for further investigation of non-linear mechanical behavior for other structures with different moduli.

Three-dimensional Behavior and Strength Characteristics of Cubical Hal-dening Materials. (입방체경화재료의 삼차원거동 및 강도특성)

  • 강병선
    • Geotechnical Engineering
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    • v.5 no.3
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    • pp.19-28
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    • 1989
  • This study has been carried out as a fundamental course for the analysis of the constitutive- equation for the materials like sands being hardened during Ehear. For this aim, experimentall tests with variable stress paths for the concrete material are performed using the cubical multi- axial test in which the three principle stresses are arbitrarily controlled. Stress-strain behaviors. and strength characteristics are suggested in octahedral planes. Various tests such as HC, CTC, . TC, 55 are performed. The main results summarized are as follows; 1. The order of strength from the largest to the smallest is CTC, TC, SS, and TE test. 2. The octahedral Ehear strength of concrete specimens is dependent upon the stress path(8) 3. There is a direct relation between strength and confining pressure. 4. The ultimate envelopes in the octahedral planes are non-circular-cone shaped. 5. Any ultimate criteria used to predict the strength behavior of concrete must include thin effect of the tensile stresses.

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Monte Carlo analysis of earthquake resistant R-C 3D shear wall-frame structures

  • Taskin, Beyza;Hasgur, Zeki
    • Structural Engineering and Mechanics
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    • v.22 no.3
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    • pp.371-399
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    • 2006
  • The theoretical background and capabilities of the developed program, SAR-CWF, for stochastic analysis of 3D reinforced-concrete shear wall-frame structures subject to seismic excitations is presented. Incremental stiffness and strength properties of system members are modeled by extended Roufaiel-Meyer hysteretic relation for bending while shear deformations for walls by Origin-Oriented hysteretic model. For the critical height of shear-walls, division to sub-elements is performed. Different yield capacities with respect to positive and negative bending, finite extensions of plastic hinges and P-${\delta}$ effects are considered while strength deterioration is controlled by accumulated hysteretic energy. Simulated strong motions are obtained from a Gaussian white-noise filtered through Kanai-Tajimi filter. Dynamic equations of motion for the system are formed according to constitutive and compatibility relations and then inserted into equivalent It$\hat{o}$-Stratonovich stochastic differential equations. A system reduction scheme based on the series expansion of eigen-modes of the undamaged structure is implemented. Time histories of seismic response statistics are obtained by utilizing the computer programs developed for different types of structures.

A Study on the Applicability of Hyperbolic Settlement Prediction Method to Consolidation Settlement in the Dredged and Reclaimed Ground (준설매립지반의 압밀침하에 대한 쌍곡선 침하예측기법의 적용성 연구)

  • Yoo, Nam-Jae;Jun, Sang-Hyun;Jeon, Jin-Yong
    • Journal of Industrial Technology
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    • v.28 no.A
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    • pp.11-17
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    • 2008
  • Applicability of hyperbolic settlement prediction method to consolidation settlement in the dredged and reclaimed ground was assessed by analyzing results of centrifuge tests modelling self-weight consolidation of soft marine clay. From literature review about self-weight consolidation of soft marine clays located in southern coast in Korea, constitutive relationships of void ratio - effective stress - permeability and typical self-weight consolidation curves with time were obtained by analyzing centrifuge model experiments. For the condition of surcharge loading, exact solution of consolidation settlement curve obtained by using Terzaghi's consolidation theory was compared with results predicted by the hyperbolic method. It was found to have its own inherent error to predict final consolidation settlement. From results of analyzing thc self-weight consolidation with time by using this method, it predicted relatively well in error range of 0.04~18% for the case of showing the linearity in the relationship between T vs T/S in the stage of consolidation degree of 60~90 %. However, it overestimated the final settlement with large errors if those relation curves were nonlinear.

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Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes

  • Daikh, Ahmed Amine;Drai, Ahmed;Houari, Mohamed Sid Ahmed;Eltaher, Mohamed A.
    • Steel and Composite Structures
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    • v.36 no.6
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    • pp.643-656
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    • 2020
  • This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.

Dynamic Material Test of Sinter-Forged Cu-Cr Alloy and Application to the Impact Characteristics of Vacuum Interrupter (구리-크롬 합금의 조성비에 따른 동적실험 및 진공 인터럽터 충격특성에의 적용)

  • Song, Jung-Han;Lim, Ji-Ho;Huh, Hoon
    • Proceedings of the KSME Conference
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    • 2004.11a
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    • pp.447-452
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    • 2004
  • Vacuum interrupters in order to be used in various switch-gear components such as circuit breakers, distribution switches, contactors, etc. spread the arc uniformly over the surface of the contacts. The electrodes of vacuum interrupters are made of sinter-forged Cu-Cr materials for good electrical and mechanical characteristics. Since the closing velocity is 1-2m/s and impact deformation of the electrode depends on the strain rate at that velocity, the dynamic behavior of the sinter-forged Cu-Cr is a key to investigate the impact characteristics of the electrodes. The dynamic response of the material at intermediate strain rate is obtained from the high speed tensile test machine test and at the high strain rate is obtained from the split Hopkinson pressure bar test. Experimental results from both quasi-static and dynamic compressive tests are interpolated to construct the Johnson-Cook model as the constitutive relation that should be applied to simulation of the dynamic behavior of the electrodes. The impact characteristics of a vacuum interrupter are investigated with computer simulations by changing the amount of chromium content.

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