• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.3A
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• pp.309-316
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• 2010

This paper proposed a nonlocal anisotropic damage model to simulate the behavior of plain and reinforced concrete structures that are predominantly tensile and compressive load. This model based on continuum damage mechanics, used a symmetric second-order tensor as the damage variable. For quasi-brittle materials, such as concrete, the damage patterns were different in tension and in compression. These two damage states were modeled by damage evolution laws ensuring a damage tensor rate proportional to the total strain tensor in terms of principal components. To investigate the effectiveness of proposed model, the double edge notched specimen experimented by nooru-mohamed and reinforced concrete bending beam were analyzed using the implementation of the proposed model. As the results for the simulation, the nonlocal anisotropic damage model with an adequate control of rupture correctly represented the crack propagation for mixed mode fracture. In the structural failure of reinforced concrete bending beam, the proposed model can be showed up to a very high damage level and yielding of the reinforcements.

• Tunnel and Underground Space
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• v.8 no.4
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• pp.275-286
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• 1998

The effective permeability and the representative element volume(REV) of fracture network model were evaluated based on the parameters such as permeability tensor, principal permeability and the direction of principal permeability. The effective permeability ranges between the harmonic mean and the arithmetic mean of the local permeabilities of subdivided blocks. From the numerical experiments, which were for investigating the influence of model volume on the variation of flux for the cubic models, it was found that the variation of flux became reduced as the model volume approached REV. The variation of groundwater flux into the tunnel in the fracture network model was mainly dependent on the ratio of the tunnel length to model size rather than REV. And it was found that groundwater flux into the tunnel was not completely consistent between the fracture network model and the equivalent porous media model, especially when the ratio of the tunnel length to model size is small.

• Journal of Soil and Groundwater Environment
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• v.7 no.2
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• pp.53-61
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• 2002

An Aquifer test was carried out on five boreholes to determine the hydrologic anisotropy and the major groundwater flow direction in the aquifer system of the study area. With an assumption of the aquifer's anisotropy and homogeneity, the major transmissivity(T(equation omitted)), the minor transmissivity( $T_{ηη}$ ), and primary tensor direction ($\theta$) for each borehole were determined from the test. Besides the boreholes BH-1, BH-4 and BH-5, the anisotropy transmissivity tensor values of BH-2 and BH-3 did not correspond with the assumption. Thereafter the values were plotted on the polar coordinate, and showed that the tensor values were out of the anisotropy ellipsoid due to the high heterogeneity of BH-2 and BH-3 comparing with the other boreholes. Therefore. the anisotropy of the aquifer was examined from BH-1, BH-4. and BH-5. In BH-1, T(equation omitted) is 171.9 $\m^2$/day. $T_{ηη}$ is $71.01\m^2$/day, and the principal tensor direction is Nl5.39$^{\circ}$E. In BH-4. T(equation omitted) is $268.2 \m^2$/day, $T_{ηη}$ / is $28.75\m^2$/day and the principal tensor direction is N7.55$^{\circ}$E. In BH-5, T(equation omitted) is $168.4\m^2$/day, $T_{ηη}$ is 66.80 $\m^2$/day, and the principal tensor direction is $N76.59^{\circ}$E. On the basis of teleview logging performed on each borehole. the principal fracture directions were revealed as $N0^{\circ}$~4$^{\circ}$E/$30^{\circ}$~$50^{\circ}$SE and $N30^{\circ}$~$80^{\circ}$W/$20^{\circ}$~$50^{\circ}$NE that are the most frequently occurred sets as well as that correspond well with the calculated transmissivity tensor.

• Journal of the Microelectronics and Packaging Society
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• v.30 no.4
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• pp.50-60
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• 2023

Ball Grid Array (BGA) is a widely used package type due to its high pin density and good heat dissipation. In BGA, solder balls play an important role in electrically connecting the package to the PCB. Therefore, understanding the inelastic deformation of solder balls under various mechanical loads is essential for the robust design of semiconductor packages. In this study, the geometrical effect on the inelastic deformation and fracture of solder balls were analyzed by finite element analysis. The results showed that fracture occurred in both tilted and hourglass shapes under shear loading, and no fracture occurred in all cases under compressive loading. However, when bending was applied, only the tilted shape failed. When shear and bending loads were combined with compression, the stress triaxiality was maintained at a value less than zero and failure was suppressed. Furthermore, a comparison using the Lagrangian-Green strain tensor of the critical element showed that even under the same loading conditions, there was a significant difference in deformation depending on the shape of the solder ball.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.7
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• pp.148-157
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• 1996

This paper deals with the applicability of linear elastic fracture mechanics under centrifugal force. Stress intensity factors K are calculated as a function of the inclination crack of length 2a, the position at different angular velocities 1200rpm, 2400rpm and at different values of the inclination crack angle .phi. ( .phi. = 0 .deg. , 15 .deg. , 30 .deg. , 45 .deg. , 60 .deg. , 75 .deg. , 90 .deg. ) and are measured in models of rotation disks using a boundary element method. Especially, stress intensity factors $K_{l}$ and $K_{ll}$ obtained separately from the crack tip of the mixed mode, were used to further investigate the influence of $K_{l}$ and $K_{ll}$ on fracture in rotating disks. With the increase in the speed of rotation, the effect of K/ sub l/became larger where as that of $K_{ll}$ became small. For the increase in the inclination crack angle .phi. , a decrease in $K_{l}$ and an increase in $K_{ll}$ were observed.

• Tunnel and Underground Space
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• v.22 no.2
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• pp.93-105
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• 2012

This paper compares the two- and three-dimensional (2D and 3D) approaches for the numerical determination of the equivalent mechanical properties of fractured rock masses. Both orthogonally-fractured model and discrete fracture networks (DFN) were used for the geometry and 2D models were cut in various directions from 3D model to compare their mechanical properties. Geological data were loosely based on the data available from Sellafield, UK. Analytical method based on compliance tensor transformation was used for investigation in orthogonally fractured rock and numerical experiments were conducted on fractured rock mass with DFN geometry. It is shown that 2D approach always overestimates the elastic modulus of fractured rock masses by a factor of up to around two because fractures are assumed to be perpendicular to the model plane in 2D problems. Poisson ratios tend to have larger values in 2D analysis while there is opposite trend in some sections. The study quantitatively demonstrates the limitation of the 2D approach that uses the simplified model from true 3D geometry.

• Economic and Environmental Geology
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• v.50 no.1
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• pp.61-71
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• 2017

The effects of joint density and size distribution on the hydrogeologic characteristics of jointed rock masses are addressed through numerical experiments based on the 2-D DFN (discrete fracture network) fluid flow analysis. Using two joint sets, a total of 51 2-D joint network system were generated with various joint density and size distribution. Twelve fluid flow directions were chosen every $30^{\circ}$ starting at $0^{\circ}$, and total of 612 $20m{\times}20m$ DFN blocks were prepared to calculate the directional block conductivity. Also, the theoretical block conductivity, principal conductivity tensor and average block conductivity for each generated joint network system were determined. The directional block conductivity and chance for the equivalent continuum behavior of the 2-D DFN system were found to increase with the increase of joint density or size distribution. However, the anisotropy of block hydraulic conductivity increases with the increase of density discrepancy between the joint sets, and the chance for the equivalent continuum behavior were found to decrease. The smaller the intersection angle of the two joint sets, the more the equivalent continuum behavior were affected by the change of joint density and size distribution. Even though the intersection angle is small enough that it is difficult to have equivalent continuum behavior, the chance for anisotropic equivalent continuum behavior increases as joint density or size distribution increases.

• Economic and Environmental Geology
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• v.49 no.1
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• pp.31-41
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• 2016

A program code was developed to calculate block hydraulic conductivity of the 2-D DFN(discrete fracture network) system based on equivalent pipe network, and implemented to examine the effect of joint orientation distribution on the hydraulic characteristics of fractured rock masses through numerical experiments. A rock block of size $32m{\times}32m$ was used to generate the DFN systems using two joint sets with fixed input parameters of joint frequency and gamma distributed joint size, and various normal distributed joint trend. DFN blocks of size $20m{\times}20m$ were selected from center of the $32m{\times}32m$ blocks to avoid boundary effect. Twelve fluid flow directions were chosen every $30^{\circ}$ starting at $0^{\circ}$. The directional block conductivity including the theoretical block conductivity, principal conductivity tensor and average block conductivity were estimated for generated 180 2-D DFN blocks. The effect of joint orientation distribution on block hydraulic conductivity and chance for the equivalent continuum behavior of the 2-D DFN system were found to increase with the decrease of mean intersection angle of the two joint sets. The effect of variability of joint orientation on block hydraulic conductivity could not be ignored for the DFN having low intersection angle between two joint sets.

• Computers and Concrete
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• v.2 no.4
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• pp.249-266
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• 2005

In the present paper a transient three-dimensional thermo-mechanical model for concrete is presented. For given boundary conditions, temperature distribution is calculated by employing a three-dimensional transient thermal finite element analysis. Thermal properties of concrete are assumed to be constant and independent of the stress-strain distribution. In the thermo-mechanical model for concrete the total strain tensor is decomposed into pure mechanical strain, free thermal strain and load induced thermal strain. The mechanical strain is calculated by using temperature dependent microplane model for concrete (O$\check{z}$bolt, et al. 2001). The dependency of the macroscopic concrete properties (Young's modulus, tensile and compressive strengths and fracture energy) on temperature is based on the available experimental database. The stress independent free thermal strain is calculated according to the proposal of Nielsen, et al. (2001). The load induced thermal strain is obtained by employing the biparabolic model, which was recently proposed by Nielsen, et al. (2004). It is assumed that the total load induced thermal strain is irrecoverable, i.e., creep component is neglected. The model is implemented into a three-dimensional FE code. The performance of headed stud anchors exposed to fire was studied. Three-dimensional transient thermal FE analysis was carried out for three embedment depths and for four thermal loading histories. The results of the analysis show that the resistance of anchors can be significantly reduced if they are exposed to fire. The largest reduction of the load capacity was obtained for anchors with relatively small embedment depths. The numerical results agree well with the available experimental evidence.

• Journal of the Korean Geotechnical Society
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• v.22 no.2
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• pp.41-53
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• 2006

The brittle materials like rocks show complicated strain-softening behavior after the peak which is hard to model using the classical constitutive models based on the relation between strain and stress tensors. A kinematically constrained three-dimensional microplane constitutive model is developed for granite. The model is verified by fitting the experimented data of Westerly granite and Bonnet granite. The triaxial behavior of granite is well reproduced by the model as well as the uniaxial behavior. We studied the development of the fracture zone in granite during blasting impact using the model with the standard finite element method. All the results obtained from the microplane model developed are compared to those from the linear elasticity model which is commonly used in many researches and practices. It is found that the nonlinearity of rocks sigificantly affects the results of analysis.