• Structural Engineering and Mechanics
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• v.83 no.4
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• pp.435-449
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• 2022

Constitutive modeling that could reasonably predict and effectively evaluate the post-peak structural behavior while eliminating the mesh-dependency in numerical simulation remains to be developed for general engineering applications. Based on the previous work, a simple one-dimensional modeling procedure is proposed to predict and evaluate the post-peak response, as characterized by the evolution of localized strain field, of a steel member to monotonically uniaxial tension. The proposed model extends the classic one-dimensional softening with localization model as introduced by (Schreyer and Chen 1986) to account for the localization length, and bifurcation and rupture points. The new findings of this research are as follows. Two types of strain-softening functions (bilinear and nonlinear) are proposed for comparison. The new failure criterion corresponding to the constitutive modeling is formulated based on the engineering strain inside the localization zone at rupture. Furthermore, a new mathematical expression is developed, based on the strain rate inside and outside the localization zone, to describe the displacement field at which bifurcation occurs. The model solutions are compared with the experimental data on four low-carbon cylindrical steel bars of different lengths. For engineering applications, the model solutions are also compared to the experimental data of a cylindrical steel bar system (three steel bars arranged in series). It is shown that the bilinear and nonlinear softening models can predict the energy dissipation in the post-peak regime with an average difference of only 4%.

• Geomechanics and Engineering
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• v.10 no.6
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• pp.827-836
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• 2016

The rate of softening is an important factor to determine whether the failure occurs along localized shear band or in a more diffused manner. In this paper, strength loss and softening rate effect depending on sensitivity are investigated for weakly cemented clays, for both artificially cemented high plasticity San Francisco Bay Mud and low plasticity Yolo Loam. Destructuration and softening behavior for weakly cemented sensitive clays are demonstrated and discussed through multiple vane shear tests. Artificial sensitive clays are prepared in the laboratory for physical modeling or constitutive modeling using a small amount of cement (2 to 5%) with controlled initial water content and curing period. Through test results, shear band thickness is theoretically computed and the rate of softening is represented as a newly introduced parameter, ${\omega}_{80%}$. Consequently, it is found that the softening rate increases with sensitivity for weakly cemented sensitive clays. Increased softening rate represents faster strength loss to residual state and faster minimizing of shear band thickness. Uncemented clay has very low softening rate to 80% strength drop. Also, it is found that higher brittleness index ($I_b$) relatively shows faster softening rate. The result would be beneficial to study of physical modeling for sensitive clays in that artificially constructed high sensitivity (up to $S_t=23$) clay exhibits faster strain softening, which results in localized shear band failure once it is remolded.

• Journal of the Korean Geosynthetics Society
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• v.2 no.1
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• pp.57-68
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• 2003

Strain-softening model is developed to characterize the interface behavior of geomembrane with geotextile and geosynthetic clay liner(GCL). The model proposed in this research is calibrated by using data from direct shear tests conducted on smooth and textured geomembrane. The research is divided into two regions, pre-peak and post-peak, to take into account of strain-softening effect. Although slight difference between measured and back calculated data is observed under high normal stress, good agreements, in general, are found from back calculations. Especially, good consistency is observed in the case of low normal stress. Based on the results, it can be concluded that the proposed model can be a reasonable constitutive law to figure out the behavior of strain-softening between interfaces of geomembrane. In addition, DSC(Disturbed State Concept) model is also presented for further application in geosynthetic interfaces.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.53-60
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• 1997

The strain localization of concrete is a phenomenon such that the deformation of concrete is localized in finite region along with softening behavior. The objective of this paper is to develope a consistent algorithm for the finite element modeling of localized zone in the analysis of the strain-localization in concrete. For modeling of the localized zone in concrete under strain localization, a general Drucker-Prager failure criterion which can consider nonlinear strain softening behavior of concrete after peak-stress is introduce. The return-mapping algorithm is used for the integration of the elasto-plastic rate equation and the consistent tangent modulus is derived. Using finite element program implemented with the developed algorithms, strain localization behaviors for the different sizes of concrete specimen under compression are simulated.

• Proceedings of the Korean Geotechical Society Conference
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• 2003.03a
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• pp.393-400
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• 2003

지오멤브레인(geomembrane)과 다른 토목섬유, 즉 지오텍스타일 또는 GCL, 사이의 interface 전단거동을 특성화하는 strain-softening 모델을 개발하였다. 본 연구에 제안된 모델은 일차적으로 smooth 지오멤브레인과 textured 지오멤브레인을 대상으로 실시한 직접전단 시험결과를 대상으로 구축되었다. 시험을 통해 측정된 변위-전단응력의 관계는 strain-softening 현상를 고려하기 위해서 최대점이 발생하는 위치를 기준으로, pre-peak과 post-peak 영역으로 나누어 분석을 실시하였다. 실험결과를 토대로 구축된 모델식은 원 자료와의 비교를 통해 본 모델의 유효성을 검증하였다. 비교 결과 높은 연직 응력에서 약간의 차이를 보이긴 하지만, 대체적으로 실험 결과와 구축된 모델을 이용한 역계산의 값이 좋은 일치를 보임을 확인할 수 있었다. 특별히 연직응력이 낮은 단계에서는 높은 일치를 보였는데, 이를 통해 제안된 식이 매립지의 최종 cover와 같이 상재 연직하중이 작은 경우에 지오멤브레인이 포함된 interface의 전단 거동에 대한 합리적인 구성 방정식이 될 수 있음을 확인할 수 있었다.

• Journal of the Korean Society of Industry Convergence
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• v.10 no.2
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• pp.81-88
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• 2007

In case of an urban tunnel, the displacement of ground base controls the tunnel design because it is built on shallow and unconsolidated ground many times. There are more insufficiency to describe the ground movement which coincides in the measured result of the situ because the design of an urban tunnel is dependent on the method of numerical analysis used to the existing elastic and elasto-plastic models. We studied about the prediction for the ground movement of a shallow tunnel in unconsolidated ground, mechanism of collapse, and settlement. Also this paper shows comparison with the existing elastic and elasto-plastic model using the unlinear analysis of the strain-softening model. We can model the real ground movement as the increasement of ground surface inclination or occurrence of shear band by using strain-softening model for the result of ground movement of an urban NATM tunnel.

• Journal of the Korean Geotechnical Society
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• v.23 no.9
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• pp.17-28
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• 2007

Urban tunnels are usually important in terms of prediction and control of surface settlement, gradient and ground displacement. This paper has studied the application of strain softening analysis to predict deformation behavior of an urban NATM tunnel. The applied strain softening model considered the reduction of shear stiffness and strength parameter after yielding with strain softening effects of a given material. Measurements of surface subsidence and ground displacement were adopted to monitor the ground behavior resulting from the tunneling and to modify tunnel design. The numerical analysis results produced a strain distribution, deformational mechanism and surface settlement profile, which are in good agreement with the results of case study. The approach of strain softening modeling is expected to be a good prediction method on the ground displacement associated with NATM tunneling at shallow depth and soft ground.

• Computational Structural Engineering
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• v.10 no.3
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• pp.241-250
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• 1997

The strain localization of concrete is a phenomenon such that the deformation of concrete is localized in finite region along with softening behavior. The objective of this paper is to develop a plasticity and damage algorithm for the finite element analysis of the strain-localization in concrete. In this paper, concrete member under strain localization is modeled with localized zone and non-localized zone. For modeling of the localized zone in concrete under strain localization, a general Drucker-Prager failure criterion by which the nonlinear strain softening behavior of concrete after peak-stress can be considered is introduced in a thermodynamic formulation of the classical plasticity model. The return-mapping algorithm is used for the integration of the elasto-plastic rate equation and the consistent tangent modulus is also derived. For the modeling of non-localized zone in concrete under strain localization, a consistent nonlinear elastic-damage algorithm is developed by modifying the free energy in thermodynamics. Using finite element program implemented with the developed algorithm, strain localization behaviors for concrete specimens under compression are simulated.

• Computational Structural Engineering
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• v.17 no.2
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• pp.20-23
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• 2004

공학적 응력-변형률 곡선에서 재료의 파괴직전에 흔히 나타나는 변형률연화 (strain softening) 현상은 국부의 집중소성변형 현상과 밀접한 관계가 있다 그러나 변형률연화는 음수의 기울기를 가지는 응력-변형률 곡선을 의미하며, 이 모델은 유한요소해석의 결과가 그 요소의 크기에 따라 수렴점이 달라지는 근본적인 문제를 가진다. 따라서 1980년대 이후 많은 학자들이 이 현상의 적절한 모델을 찾기 위한 노력을 기울여왔다. (중략)

• Computational Structural Engineering
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• v.17 no.3
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• pp.22-27
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• 2004