• Geomechanics and Engineering
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• v.7 no.4
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• pp.335-353
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• 2014

The softening hyperelastic model based on the strain energy limitation is of clear concepts and simple forms to describe the failure of materials. In this study, a linear and a nonlinear softening hyperelastic model are proposed to characterize the deformation and the failure in granular materials by introducing a softening function into the shear part of the strain energy. A method to determine material parameters introduced in the models is suggested. Based on the proposed models the numerical examples focus on bearing capacity and strain localization of granular materials. Compared with Volokh softening hyperelasticity and classical Mohr-Coulomb plasticity, our proposed models are able to capture the typical characters of granular materials such as the strain softening and the critical state. In addition, the issue of mesh dependency of the proposed models is investigated.

• Coupled systems mechanics
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• v.4 no.3
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• pp.211-235
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• 2015

In this work we present a one-dimensional damage model capable of representing the dynamic fracture for elastodamage bar with combined hardening in fracture process zone - FPZ and softening with embedded strong discontinuities. This model is compared with another one we recently introduced (Do et al. 2015) and it shows a good agreement between two models. Namely, it is indicated that strain-softening leads to a sensitivity of results on the mesh discretization. Strain tends to localization in a single element which is the smallest possible area in the finite element simulations. The strain-softening element in the middle of the bar undergoes intense deformation. Strain increases with increasing mesh refinement. Strain in elements outside the strain-softening element gradually decreases to zero.

• Coupled systems mechanics
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• v.4 no.2
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• pp.115-136
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• 2015

We present for one-dimensional model for elastoplastic bar with combined hardening in FPZ - fracture process zone and softening with embedded strong discontinuities. The simplified version of the model without FPZ is directly compared and validated against analytical solution of Bazant and Belytschko (1985). It is shown that deformation localizes in an area which is governed by the chosen element size and therefore causes mesh sensitivity and that the length of the strain-softening region tends to localize into a point, which also agrees with results obtained by stability analysis for static case. Strain increases in the softening domain with a simultaneous decrease of stress. The problem unloads elastically outside the strain-softening region. The more general case with FPZ leads to more interesting results that also account for induced strain heterogeneities.

• Transactions of Materials Processing
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• v.4 no.2
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• pp.169-179
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• 1995

Static restoration mechanism during hot interrupted deformation of Cu-Zn alloy was studied in the temperature range from $550^{\circ}C$ to $750^{\circ}C$ and at a constant strain rate of 0.1/sec. At a given temperature, the hot interrupted deformations were performed with variation of interrupted time $t_i$ form 1 to 50 sec and of interrupted strain ${\varepsilon}_i$ from 0.15 to 0.90. From the analysis of the values of the critical strain of ${\varepsilon}_c$ for tje initiation of dynamic recrystallization and the peak strain of${\varepsilon}_p$, the relationship ${\varepsilon}_c{\fallingdotseq}0.7{\varepsilon}_p$ was obtained. It was clarified that the softening of the interrupted deformation was mainly the static recrystallization and the fractional softening(FS) which was over 30% mostly confirmed this result. The fractional softening of the interrupted time $t_i$ especially and pre-strain. The FS increased with increasing strain rate, interrupted time and pre-strain. The change of microstructures after hot deformation could be predicted by the FS. when the FS was 30~100%, static recrystallization was happened and grain growth was observed at the condition which was $750^{\circ}C$ deformation temperature, 0.45 prestrain and this condition's FS value was over 100%.

• Journal of Advanced Marine Engineering and Technology
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• v.27 no.4
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• pp.494-502
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• 2003

The near-tip field of mode-I dynamic cracks steadily propagating in a strain softening material is investigated under plane strain conditions. The material is assumed to be incompressible and its deformation obeys the $J_2$ flow theory of plasticity. A power-law stress-strain relation with strain softening is adopted to account for the damage behavior of materials near the dynamic crack tip. By assuming that the stresses and strain have the same singularity at the crack tip. this paper obtains a fully continuous dynamic crack-tip field in the damage region. Results show that the stress and strain components the same logarithmic singularity of (In(R/r))$\delta$, and the angular variations of filed quantities are identical to those corresponding to the dynamic cracks in the elastic-perfectly plastic material.

• Geomechanics and Engineering
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• v.18 no.3
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• pp.225-234
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• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

• Computers and Concrete
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• v.9 no.1
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• pp.35-50
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• 2012

The 2D representative volume element (RVE) for softening quasi-brittle materials like concrete is determined. Two alternative methods are presented to determine a size of RVE in concrete subjected to uniaxial tension by taking into account strain localization. Concrete is described as a heterogeneous three-phase material composed of aggregate, cement matrix and bond. The plane strain FE calculations of strain localization at meso-scale are carried out with an isotropic damage model with non-local softening.

• Geotechnical Engineering
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• v.13 no.2
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• pp.29-38
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• 1997

Strain softening is observed for geomaterials such as rocks when they are sheared. The proper computational modelling for strain softening is very important because this behavior is closely related to failure in geotechnical problems. In this paper, we have investigated the proper FEM techniques for modelling strain softening in order to simulate failure behavior numerically. In showing numerical examples, the effects of element shape, mesh pattern and of imperfection and the difference between small and large deformation theories, of displacement control and pressure control after peak have been discussed.

• Transactions of Materials Processing
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• v.10 no.1
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• pp.35-41
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• 2001

The high temperature deformation behavior of SCM 440 can be characterized by the hot torsion test in the temperature ranges of $900^{\circ}C$~$1100^{\circ}C$ and strain rate ranges of 0.05/sec~5/sec. The aim of this paper is to establish the quantitative equation of the volume fraction of dynamic recrystallization (DRX) as a function of processing variables, such as strain rate ($\varepsilon$), temperature (T), and strain ('$\varepsilon$). During hot deformation, the evolution of microstructure could be analyzed from work hardening rate ($\theta$). For the exact prediction of dynamic softening mechanism the critical strain ($\varepsilon_c$), the strain for maximum softening rate ($\varepsilon^*$ and Avrami' exponent (m') were quantitatively expressed by dimensionless parameter, Z/A, respectively. The transformation-effective strain-temperature curve for DRX could be composed. It was found that the calculated results were agreed with the experimental data for the steel at any deformation conditions.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1995.10a
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• pp.172-180
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• 1995

Isothermal interrupted deformation behavior of 10vol.%SICp/AI-Si composites was investigated by hot torsion test at the temperature ranges from 27$0^{\circ}C$ to 43$0^{\circ}C$ and at strain rate range of 1.26X10-2~2.16X10-1/sec. With increasing pass strain, flow stresses were high compared to continuous deformation condition. Fractional softening was increased with temperature imterruption time and pass strain. Fractional softening of 10vol.%SiCp/AI-Si composites was lower than that of AI-Si matrix at 37$0^{\circ}C$. However at high temperature of 43$0^{\circ}C$, SiC particle promoted static softening, diminishing the dislocation density at the interface of AI-Si matrix and reinforcements, then this resulted in higher fractional softening in composites. Both of failure strain improved reducing the fracture of SiC particle and Si precipitates above 32$0^{\circ}C$, however at low temperature of 27$0^{\circ}C$, the softening effect by interrupted deformation was found to be negligible.