• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.215-219
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• 2003

Buckling and post-buckling Analysis of Ludwick type and modified Ludwick type elastic materials was carried out. Because the constitutive equation, or stress-strain relationship is different from that of linear elastic one, a new governing equation was derived and solved by $4^{th}$ order Runge-Kutta method. Considered as a special case of combined loading, the buckling under both point and distributed load was selected and researched. The final solution takes distinguished behavior whether the constitutive relation is chosen to be modified or non-modified Ludwick type as well as linear or non-linear. We also derived strain energy function for non-linear elastic constitutive relationship. By doing so, we calculated the criterion function which estimates the stability of the equilibrium solutions and determines critical buckling load for non-linear cases. We applied this theory to the constitutive relationship of fabric, which also is the non-linear equation between the applied moment and curvature. This results has both technical and mathematical significance.

• Geomechanics and Engineering
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• v.24 no.3
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• pp.295-305
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• 2021

In this study, design charts for estimating consolidation settlement are proposed according to finite strain consolidation theory using a nonlinear constitutive relationship equation. Results of parametric sensitivity analysis shows that the final settlement, initial height, and initial void ratio exerted the greatest effect, and the coefficients of the void ratio-effective-stress. Proposed design charts were analyzed for three regions using a representative constitutive relationship equation that enables major dredged-reclaimed construction sites in Korea. The regional design charts can be calculated accurately for the final settlement because it is applied directly to the numerical analysis results, except for reading errors. A general design chart applicable to all marine clays is proposed through correlation analysis of the main parameters. A final self-weight consolidation settlement with various initial void ratios and initial height conditions should be estimated easily using the general design chart and constitutive relationship. The estimated final settlement using the general design chart is similar to the results of numerical analysis obtained using finite strain consolidation theory. Under an overburden pressure condition, design charts for estimating consolidation settlement are proposed for three regions in Korea.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.92-98
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• 1998

Nonlinear finite element analyses of one dimensional consolidation problem were performed using an anisotropic hardening constitutive model. For the analyses, the anisotropic hardening elasto-plastic constitutive model based on the generalized isotropic hardening(GIH) rule was implemented into a nonlinear finite element analysis program, PLASTIC. In order to preserve the accuracy of the finite element solution for nonlinear problems, an implicit stress integration algorithm was employed. A consistent tangent moduli could also ensure the quadratic convergence of Newton's method. As a result, the nonlinear solution was accurately calculated and was converged to be asymptotically quadratic. In a consolidation problem, the relationship between load and settlement and between settlement and time vertical was analyzed comparing with results using the Cam-clay type model and the final consolidation settlement and the duration of primary consolidation could be evaluated rigorously using the GIH constitutive model.

• Geomechanics and Engineering
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• v.1 no.4
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• pp.263-274
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• 2009

The modified Cam clay (MCC) model is used to study the response of virgin compressed clay in undrained compression. The MCC deviatoric stress-strain relationship is obtained in closed form. Elastic and plastic deviatoric strains are taken into account in the analysis. For the determination of the elastic strain components, both a variable shear modulus and constant shear modulus are considered. Constitutive relationships are applied to the well-known London and Weald clays sheared in undrained compression.

• Geomechanics and Engineering
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• v.25 no.2
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• pp.75-87
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• 2021

Because the hydraulic/mechanical behaviour of unsaturated soil is more complicated than that of saturated soil, one of the most important issues in modelling unsaturated soil is to properly couple its stress-strain relationship with its water retention characteristics. Based on the results of a series of tests, the stress-strain relationship and the changes in suction and saturation of unsaturated completely decomposed granite (CDG, also called Masado) vary substantially under different loading/hydraulic conditions. To precisely model the hydraulic/mechanical behaviour of unsaturated Masado, in this study, the superloading concept was firstly introduced into an existing saturated/unsaturated constitutive model to consider the structural influences. Then a water retention curve (WRC) model considering the volumetric change in the soil, in which the skeleton and scanning curves of the water retention characteristics were assumed to shift in parallel in accordance with the change in the void ratio, was proposed. The proposed WRC model was incorporated into the constitutive model, and the validity of the newly proposed model was verified using the results of tests conducted on unsaturated Masado, including water retention, oedometer and triaxial tests. The accuracy of the proposed model in describing the stress-strain relationship and the variations in suction and saturation of unsaturated Masado is satisfactory.

• Geotechnical Engineering
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• v.12 no.4
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• pp.145-156
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• 1996

An implicit stress integration algorithm was formulated for implementing an aiusotorpic hardening constitutive model which has been based op the generalized isotropic hardening rule in nonlinear finite element analysis technique. the rate form of stress tensor was implicitly integrated using the generalized trapezoidal rule and the tangent stress-strain modulus was evaluated consistently with the nonlinear solution technique. As a result, it has been found that the nonlinear analysis with the anisotropic hardening constitutive model might be performed accurately and efficiently.

• Journal of the Korea Concrete Institute
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• v.22 no.4
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• pp.481-488
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• 2010

Since existing constitutive models developed for confined normal strength concrete overestimate ductility when they are applied to confined high strength concrete, these models cannot be directly applied to confined high strength concrete. In an effort to solve this problem, an accurate stress-strain relationship of the hihg strength concrete needs to be formulated by examining the confinement effects due to increase of the concrete strength. In this study, a constitutive model is developed to express the stress-strain relationship of confined high strength concrete by carrying out regression analysis of the main parameters affection strength and ductile behavior of reinforced high strength concrete columns. Twenty-five test specimens were chosen from the reported experimental studies in the literature. The experimental results of stress-strain relationships of show a good agreement with results of the stress-strain relationships of suggested high strength concrete, covering a strength range between 60 and 124 MPa.

• 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.

• KCI Concrete Journal
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• v.12 no.2
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• pp.55-72
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• 2000

This paper proposes a mechanical model to describe the load-deformation responses of the reinforced concrete plate members under service load state. An Analytical method is introduced on the basis of the rotating crack model which considers equilibrium, compatibility conditions, load-strain relationship of cracked member, and constitutive law for materials. The tension stiffening effect in reinforced concrete structures is taken into account by the average tensile stress-strain relationship from the load-strain relationship for the cracked member and the constitutive law for material. The strain compatibility is used to find out the crack direction because the crack direction is an unknown variable in the equilibrium and compatibility conditions. The proposed theory is verified by the numerous experimental data such as the crack direction, moment-steel strain relationship, moment-crack width relationship. The present paper can provide some basis for the provision of the definition of serviceability for plate structures of which reinforcements are deviated from the principal stresses, because the present code defines the serviceability by the deflection, crack control, vibration and fatigue basically for the skeletal members. The proposed theory is applicable to predict the service load state behavior of a variety of reinforced concrete plate structures such as skew slab bridges, the deck of skew girder bridges.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.724-727
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• 1995

Dynamic deformation behavior under the high strain rate loading condition obtained with the aid of Split Hopkinson Pressure Bar(SHPB) technique is simulated by DYNA2D (an hydrodynamic code). A constitutive equation such as Johnson-Cook model is used by adjusting various parameters to fit experimentally determined dynamic stress-strain relationship.