• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.69-89
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• 2009

Reinforced and prestressed concrete (RC and PC) thin walls are crucial to the safety and serviceability of structures subjected to shear. The shear strengths of elements in walls depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. The past three decades have seen a rapid development of knowledge in shear of reinforced concrete structures. Various rational models have been proposed that are based on the smeared-crack concept and can satisfy Navier's three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility and constitutive laws). The Cyclic Softened Membrane Model (CSMM) is one such rational model developed at the University of Houston, which is being efficiently used to predict the behavior of RC/PC structures critical in shear. CSMM for RC has already been implemented into finite element framework of OpenSees (Fenves 2005) to come up with a finite element program called Simulation of Reinforced Concrete Structures (SRCS) (Zhong 2005, Mo et al. 2008). CSMM for PC is being currently implemented into SRCS to make the program applicable to reinforced as well as prestressed concrete. The generalized program is called Simulation of Concrete Structures (SCS). In this paper, the CSMM for RC/PC in material scale is first introduced. Basically, the constitutive relationships of the materials, including uniaxial constitutive relationship of concrete, uniaxial constitutive relationships of reinforcements embedded in concrete and constitutive relationship of concrete in shear, are determined by testing RC/PC full-scale panels in a Universal Panel Tester available at the University of Houston. The formulation in element scale is then derived, including equilibrium and compatibility equations, relationship between biaxial strains and uniaxial strains, material stiffness matrix and RC plane stress element. Finally the formulated results with RC/PC plane stress elements are implemented in structure scale into a finite element program based on the framework of OpenSees to predict the structural behavior of RC/PC thin-walled structures subjected to earthquake-type loading. The accuracy of the multiscale modeling technique is validated by comparing the simulated responses of RC shear walls subjected to reversed cyclic loading and shake table excitations with test data. The response of a post tensioned precast column under reversed cyclic loads has also been simulated to check the accuracy of SCS which is currently under development. This multiscale modeling technique greatly improves the simulation capability of RC thin-walled structures available to researchers and engineers.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.3
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• pp.325-333
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• 2015

Recently, thermal bridge breaker systems(TBBSs) applicable to RC slab-wall connections have been increasingly studied and proposed. This study also aims at proposing an analytic model which is applicable to predicting the flexural behavior of TBBS embedded in slabs from the initial elastic stages, yield states to ultimate conditions. The analytic models are developed by considering strain compatibility, force equilibrium and the constitutive law obtained from material test results. To verify the accuracy of the proposed analytic model, the moment-curvature relationship and change of neutral axis according to the loading states are compared with those of experimental results. Based on the comparison, it is verified that the proposed analytic model provides well predict the flexural behavior of TBBS embedded in slabs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.795-802
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• 2002

For assessing significance of a defect in a component operating at high (creeping) temperatures, accurate estimation of fracture mechanics parameter, $C^{*}$-integral, is essential. Although the J estimation equation in the GE/EPRl handbook can be used to estimate the $C^{*}$-integral when the creep -deformation behavior can be characterized by the power law creep, such power law creep behavior is a very poor approximation for typical creep behaviors of most materials. Accordingly there can be a significant error in the $C^{*}$-integral. To overcome problems associated with GE/EPRl approach, the reference stress approach has been proposed, but the results can be sometimes unduly conservative. In this paper, a new method to estimate the $C^{*}$-integral for deflective components is proposed. This method improves the accuracy of the reference stress approach significantly. The proposed calculations are then validated against elastic -creep finite element (FE) analyses for four different cracked geometries following various creep -deformation constitutive laws. Comparison of the FE $C^{*}$-integral values with those calculated from the proposed method shows good agreements.greements.

• Computers and Concrete
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• v.5 no.4
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• pp.329-342
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• 2008

A local behavior law, which includes elasticity, plasticity and damage, is developed in a three dimensional numerical model for concrete. The model is based on the Discrete Element Method (DEM)and the computational implementation has been carried out in the numerical Code YADE. This model was used to study the response of a concrete slab impacted by a rigid missile, and focuses on the extension of the compacted zone. To do so, the model was first used to simulate compression and hydrostatic tests. Once the local constitutive law parameters of the discrete element model were calibrated, the numerical model simulated the impact of a rigid missile used as a reference case to be compared to an experimental data set. From this reference case, simulations were carried out to show the importance of compaction during an impact and how it expands depending on the different impact conditions. Moreover, the numerical results were compared to empirical predictive formulae for penetration and perforation cases, demonstrating the importance of taking into account the local compaction process in the local interaction law between discrete elements.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Computational Structural Engineering : An International Journal
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• v.1 no.2
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• pp.107-116
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• 2001

The present paper investigates the nonlinear behavior of reinforced concrete shear walls with a crank based on a finite element analysis. The loading type is a horizontal cyclic one such as earthquake loads. Experiments of the shear walls with and without cranks, performed previously to see flow the behavior changes depending on the crank, are compared with the results obtained from the finite element analysis. The finite element analysis is based on an isoparametric degenerated shell formulation. The nonlinear constitutive equations fur concrete are modeled adopting the formulation based on a concept of Ring Typed-Lattice Model. The experiments indicate that the shear walls with a crank have low stiffness and relatively low carrying capacity compared with an ordinary plane shear wall without cranks and that they are more ductile, and the tendency is a1so confirmed based on the finite element analysis. Moreover, a good agreement between the experiments and analyses is obtained, accordingly, it is confined that the present numerical analysis scheme based on the Lattice Model is a powerful one to evaluate the behavior of reinforced concrete shear walls with cranks and without cranks.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.313-328
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• 2002

Based on the orthotropic hypoelasticity formulation, a triaxial constitutive model of concrete is proposed. To account for increasing ductility in high confinement of concrete, the ductility enhancement is considered using so called the strain enhancement factor. It is also developed a three-dimensional finite element model for reinforced concrete structural members based on the proposed constitutive law of concrete with the smeared crack approach. The concrete confinement effects due to the beam-column joint are investigated through numerical examples for simple beam and structural beam member. Concrete at compression fibers in the vicinity of beam-column joint behaves dominant not only by the uniaxial compressive state but also by the biaxial and triaxial compressive states. For the reason of the severe confinement of concrete in the beam-column joint, the flexural critical cross-section is observed at a small distance away from the beam-column joint. These observations should be utilized for the economic design when the concrete structural members are subjected to high confinement due to the influence of beam-column joint.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.65-74
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• 2003

This paper presents the results of a comparative study between FEM and LEM on slope stability analysis. For validation, factors of safety were compared between FEM and LEM. The results from the two methods were in good agreement. This suggests that the FEM with the shear strength reduction method can be effectively used on slope stability analyses. A series of analyses were then performed using the FEM for various constitutive laws, slope angles, flow rules, and the finite element discretizations. Among the findings, the finite element method in conjunction with the shear strength reduction method can provide reasonable results in terms of safety. Also revealed is that the results of FEM can be significantly affected by the way in which the type of constitutive law and flow nile we selected.

• Journal of the Korea Concrete Institute
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• v.17 no.6 s.90
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• pp.1053-1064
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• 2005

The mechanical damage of concrete is normally attributed to the formation of microcracks and their propagation and coalescence into macroscopic cracks. This physical degradation is caused from progressive and hierarchical damage of the microstructure due to debonding and slip along bimaterial interfaces at the mesoscale. Their growth and coalescence leads to initiation of hairline discrete cracks at the mesoscale. Eventually, single or multiple major discrete cracks develop at the macroscale. In this paper, from this conceptual model of mechanical damage in concrete, the computational efforts were made in order to characterize physical cracks and how to quantify the damage of concrete materials within the laws of thermodynamics with the aid of interface element in traditional finite element methodology. One dimensional effective traction/jump constitutive interface law is introduced in order to accommodate the normal opening and tangential slips on the interfaces between different materials(adhesion) or similar materials(cohesion) in two and three dimensional problems. Mode I failure and mixed mode failure of various geometries and boundary conditions are discussed in the sense of crack propagation and their spent of fracture energy under monotonic displacement control.

• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.675-696
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• 2009

In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.