• Steel and Composite Structures
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• v.23 no.3
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

• Coupled systems mechanics
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• v.6 no.1
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• pp.97-111
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• 2017

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.4
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• pp.1-11
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• 1984

Developed is a nonlinear fracture theory which can model the complex fracture behavior of concrete. This theory is based on the nonlinear behavior due to progressive microcracking and strain-softening in the fracture process zone of concrete cracks. The simplified realistic fracture model which preserves the same fracture energy for the different fracture process zone widths is also derived. By modeling fracture through stress-strain behavior, the effect of compressive stresses parallel to the crack plane can be easily taken into account. The comparisons of the present theory with valuable fracture test data available in the literature show good agreements, and the existing linear theory exhibits in many cases large deviations from the actual test results. A simple approximate formula for the fracture energy of concrete which should, be necessary for the fracture analysis of concrete structures is derived. Finally, the application of fracture theory to reinforced concrete and the necessity of further research are discussed.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.227-244
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• 1994

The purpose of this investigation is to propose a numerical simulation method of the crack propagation behavior in 3-dimensionl elastic body. The simulation method is based on the displacement-type finite element method, and the linear fracture theory is introduced. The results from the proposed method are compared with those from the structural experiments, and the good coincidences between them are shown in this paper. At the same time, 2-dimensional analysis is also done, and the results are compared with those obtained from 3-dimensional analysis and the structural experiments.

• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.65-72
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• 2001

This paper demonstrates an explicit-implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for an existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory. Darcy's law is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full Newton-Raphson method is used for solving the nonlinear governing equations.

• Computers and Concrete
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• v.27 no.1
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• pp.55-62
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• 2021

The concrete fatigue analysis can be performed with the use of fracture mechanics. The fracture mechanics defines the fatigue crack propagation as the relationship of crack growth rate and stress intensity factor. In contrast to metal, the application of fracture mechanics to concrete is more complicated and therefore many authors have introduced empirical expressions using Paris law. The topic of this paper is development of a new prediction of fatigue crack propagation for concrete using rheological-dynamical analogy (RDA) and finite element method (FEM) in the frame of linear elastic fracture mechanics (LEFM). The static and cyclic fatigue three-point bending tests on notched beams are considered. Verification of the proposed approach was performed on the test results taken from the literature. The comparison between the theoretical model and experimental results indicates that the model proposed in this paper is valid to predict the crack propagation in flexural fatigue of concrete.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.42-49
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• 1999

Because the linear elastic tincture analysis has been proved to be insufficient in predicting the failure of cracked bodies, in recent years, a number of fracture concepts have been studied which remain applicable in the presence of large-scale plasticity near a crack tip. This work thereby presents a new finite element model, as accurate as possible, to analyze plane problems of ductile fracture under large-scale yielding conditions. Based on the incremental theory of plasticity, the p-version finite element analysis is employed to account for the values of J-integral, the most dominant fracture parameter, and the shape of plastic zone near a crack tip by using the J-integral method and equivalent domain integral method. The numerical results by the proposed model are compared with the theoretical solutions in literatures and the numerical solutions by the i,-version of F.E.M.

• Journal of the Korea Concrete Institute
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• v.12 no.3
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• pp.31-37
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• 2000

When a crack is produced in a concrete structure, a micro crack zone of fracture process zone (FPZ) appears at the crack tip. To investigate the behaviour of this the micro crack zone, nonlinear fracture mechanics (NLFM) must be applied. However, when a massive concrete structure such as a concrete gravity dam is considered, the micro crack zone can be neglected and the structure can be assumed to have linear elastic fracture mechanics (LEFM) behaviour. This study is divided into two main topics : (1) Calculating stress intensity factor (SIF) at the crack tip by surface integral method and (2) Investigating the propagation of the initial crack. If the initial crack propagates, the angle of the propagation is calculated by using maximum circumferential tensile strength theory. This study, also, contains the effects of body forces and water pressures on the crack face.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.749-765
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• 2008

Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love's first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.

• Computers and Concrete
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• v.5 no.4
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• pp.401-416
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• 2008

The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 3D composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.