• 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%.

• Journal of Welding and Joining
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• v.9 no.2
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• pp.44-50
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• 1991

The use of high tensile steel plates is increasing in the fabrication of ship and offshore structures. The softening region which has lower yield stress than base metal is located to prevent cracking in the conventional high tensile steel. Also, thermo mechanical control process(TMCP) steel with low carbon equivalent has the softening region which occurs in the heat affected zone when high heat input weld is carried out. The softening region in the high tensile steel gives rise to serious effect on structural strength such as tensile strength, fatigue strength and ultimate strength. In order to make a reliable structural design using high tensile steel plates, the influence of the softening on plate strength should be evaluated in advance. In the previous paper, the authors discussed the ultimate compressive strength of 50HT steel square plates with softening region. In this paper, the ultimate compressive strength with varying the yield stress of softening region and the aspect ratio of the plate is investigated by using the elasto-plastic large deformation finite element method.

• 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 Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.304-307
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• 2008

In order to evaluate the effect of permanent softening behavior on springback prediction, 2D-draw bending simulations were compared with experiments for friction stir welded DP590 steel sheets. To account fur the nonlinear hardening behavior, the combined isotropic-kinematic hardening law was utilized with and without considering the permanent softening behavior during reverse loading. Also, the non-quadratic orthotropic yield function, Yld2000-2d, was used to describe the anisotropic initial-yielding behavior of the base sheet while anisotropic properties of the weld zone were ignored for simplicity.

• 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.

• Structural Engineering and Mechanics
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• v.11 no.6
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• pp.591-604
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• 2001

In this paper, a finite element with embedded displacement discontinuity which eliminates the need for remeshing of elements in the discrete crack approach is applied for the progressive fracture analysis of concrete structures. A finite element formulation is implemented with the extension of the principle of virtual work to a continuum which contains internal displacement discontinuity. By introducing a discontinuous displacement shape function into the finite element formulation, the displacement discontinuity is obtained within an element. By applying either a nonlinear or an idealized linear softening curve representing the fracture process zone (FPZ) of concrete as a constitutive equation to the displacement discontinuity, progressive fracture analysis of concrete structures is performed. In this analysis, localized progressive fracture simultaneous with crack closure in concrete structures under mixed mode loading is simulated by adopting the unloading path in the softening curve. Several examples demonstrate the capability of the analytical technique for the progressive fracture analysis of concrete structures.

• Proceedings of the Korea Concrete Institute Conference
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• 1992.10a
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• pp.173-178
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• 1992

Ficticious Crack Model(FCM) is one of the Nonlinear Analysis Method which is presented strictly strain softening phenomena of concrete in the fracture zone. As no stress singularities occur, it is not necessary to use special crack tip elements for this analysis. A special feature of the used method is that it explains not only the growth of existing cracks, but also the formation of new crack, as it is assumed that cracks start forming when the tensile stress reaches ft, i, e the same criterion is used for formation and propagation of cracks.

• Journal of the Korean Society for Heat Treatment
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• v.9 no.4
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• pp.229-233
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• 1996

This work has been carried out to reduce the softening of heat affected zone on laser surface alloying. Iron based rapid solidification material with $Cr_{5-10}$, $V_{1-3}$, $Mo_{3-7}$, $W_{2-5}$, $B_{7-8}$, $C_{2-3}$, $Si_{0.5-1}at%$ was alloyed on the surface of SM45C steel. The excellent softening resistance in alloyed and heat affected zone showed, which could be attributed to the formation of stable high temperature precipitates.

• Coupled systems mechanics
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• v.7 no.6
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• pp.669-690
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• 2018

This paper deals with numerical modeling of dynamic failure phenomena in rate-sensitive brittle and/or ductile materials. To this end, a two-dimensional continuum viscodamage-embedded discontinuity model, which is based on our previous work (see Do et al. 2017), is developed. More specifically, the pre-peak nonlinear and rate-sensitive hardening response of the material behavior, representing the fracture-process zone creation, is described by a rate-dependent continuum damage model. Meanwhile, an embedded displacement discontinuity model is used to formulate the post-peak response, involving the macro-crack creation accompanied by exponential softening. The numerical implementation in the context of the finite element method exploiting the second-order mid-point scheme is discussed in detail. In order to show the performance of the model several numerical examples are included.

• Computers and Concrete
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• v.1 no.1
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• pp.47-60
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• 2004

The influence of the fracture process zone (FPZ) on the fracture properties is one of the hottest topics in the field of fracture mechanics for cementitious materials. Within the FPZ in front of a traction free crack, cohesive forces are distributed in accordance with the softening stress-separation constitutive relation of the material. Therefore, further crack propagation necessitates energy dissipation, which is the work done by the cohesive forces. In this paper $g_f$, the local fracture energy characterizing the energy consumption due to the cohesive forces, is discussed. The computational expression of $g_f$ in the FPZ can be obtained for any stage during the material fracture process regarding the variation of FPZ, whether in terms of its length or width. $G_{fa}$, the average energy consumption along the crack extension region, has also been computed and discussed in this paper. The experimental results obtained from the wedge splitting tests on specimens with different initial notch ratios are employed to investigate the property of the local fracture energy $g_f$ and the average value $G_{fa}$ over the crack extension length. These results can be used to indicate the influence of the FPZ. Additionally, changes in the length of the FPZ during the fracture process are also studied.