• Coupled systems mechanics
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• v.7 no.6
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• pp.669-690
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• 2018

This paper deals with numerical modeling of dynamic failure phenomena in rate-sensitive brittle and/or ductile materials. To this end, a two-dimensional continuum viscodamage-embedded discontinuity model, which is based on our previous work (see Do et al. 2017), is developed. More specifically, the pre-peak nonlinear and rate-sensitive hardening response of the material behavior, representing the fracture-process zone creation, is described by a rate-dependent continuum damage model. Meanwhile, an embedded displacement discontinuity model is used to formulate the post-peak response, involving the macro-crack creation accompanied by exponential softening. The numerical implementation in the context of the finite element method exploiting the second-order mid-point scheme is discussed in detail. In order to show the performance of the model several numerical examples are included.

• Journal of the Korea Concrete Institute
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• v.11 no.3
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• pp.181-192
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• 1999

The progressive failure following strain localization in concrete can be analyzed effectively using finite element modeling of fracture process zone of concrete with a finite element embedded discontinuity. In this study, a finite element with embedded discontinuous line is utilized for the analysis of progressive failure in concrete. The finite element with embedded discontinuity is a kind of discrete crack element, but the difficulties in discrete crack approach such as remeshing or adding new nodes along with crack growth can be avoided. Using a discontinuous shape function for this element, the displacement discontinuity is embedded within an element and its constitutive equation is modeled from the modeling of fracture process zone. The element stiffness matrix is derived and its dual mapping technique for numerical integration is employed. Then, a finite element analysis program with employed algorithms is developed and failure analysis results using developed finite element program are verified through the comparison with experimental data and other analysis results.

• Structural Engineering and Mechanics
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• v.11 no.6
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• pp.591-604
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• 2001

In this paper, a finite element with embedded displacement discontinuity which eliminates the need for remeshing of elements in the discrete crack approach is applied for the progressive fracture analysis of concrete structures. A finite element formulation is implemented with the extension of the principle of virtual work to a continuum which contains internal displacement discontinuity. By introducing a discontinuous displacement shape function into the finite element formulation, the displacement discontinuity is obtained within an element. By applying either a nonlinear or an idealized linear softening curve representing the fracture process zone (FPZ) of concrete as a constitutive equation to the displacement discontinuity, progressive fracture analysis of concrete structures is performed. In this analysis, localized progressive fracture simultaneous with crack closure in concrete structures under mixed mode loading is simulated by adopting the unloading path in the softening curve. Several examples demonstrate the capability of the analytical technique for the progressive fracture analysis of concrete structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.4
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• pp.283-288
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• 2017

A spot welded joint is modeled using 3-D finite elements with embedded strong discontinuities. The spot weld is represented by a special cohesive law on the embedded discontinuity surface, instead of meshing its geometry. This strategy naturally eliminates the need of adaptive FEM meshes fitting the local geometry of the spot weld. Mesh independent solutions are guaranteed by explicitly modeling the detailed shape of the spot weld, which is in contrast with the exiting approach using point constraints for the spot weld.

• Computers and Concrete
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• v.7 no.6
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• pp.483-496
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• 2010

This work deals with the determination of crack openings in 2D reinforced concrete structures using the Finite Element Method with a smeared rotating crack model or an embedded crack model. In the smeared crack model, the strong discontinuity associated with the crack is spread throughout the finite element. As is well known, the continuity of the displacement field assumed for these models is incompatible with the actual discontinuity. However, this type of model has been used extensively due to the relative computational simplicity it provides by treating cracks in a continuum framework, as well as the reportedly good predictions of reinforced concrete members' structural behavior. On the other hand, by enriching the displacement field within each finite element crossed by the crack path, the embedded crack model is able to describe the effects of actual discontinuities (cracks). This paper presents a comparative study of the abilities of these 2D models in predicting the mechanical behavior of reinforced concrete structures. Structural responses are compared with experimental results from the literature, including crack patterns, crack openings and rebar stresses predicted by both models.

• Computers and Concrete
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• v.12 no.3
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• pp.261-283
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• 2013

This paper aims to contribute to the three-dimensional generalization of numerical prediction of crack propagation through the formulation of finite elements with embedded discontinuities. The analysis of crack propagation in two-dimensional problems yields lines of discontinuity that can be tracked in a relatively simple way through the sequential construction of straight line segments oriented according to the direction of failure within each finite element in the solid. In three-dimensional analysis, the construction of the discontinuity path is more complex because it requires the creation of plane surfaces within each element, which must be continuous between the elements. In the method proposed by Chaves (2003) the crack is determined by solving a problem analogous to the heat conduction problem, established from local failure orientations, based on the stress state of the mechanical problem. To minimize the computational effort, in this paper a new strategy is proposed whereby the analysis for tracking the discontinuity path is restricted to the domain formed by some elements near the crack surface that develops along the loading process. The proposed methodology is validated by performing three-dimensional analyses of basic problems of experimental fractures and comparing their results with those reported in the literature.

• Coupled systems mechanics
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• v.8 no.2
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• pp.111-127
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• 2019

In this paper, we present a 2D multi-scale coupling computation procedure for localized failure. When modeling the behavior of a structure by a multi-scale method, the macro-scale is used to describe the homogenized response of the structure, and the micro-scale to describe the details of the behavior on the smaller scale of the material where some inelastic mechanisms, like damage or plasticity, can be defined. The micro-scale mesh is defined for each multi-scale element in a way to fit entirely inside it. The two scales are coupled by imposing the constraint on the displacement field over their interface. An embedded discontinuity is implemented in the macro-scale element to capture the softening behavior happening on the micro-scale. The computation is performed using the operator split solution procedure on both scales.

• Journal of Positioning, Navigation, and Timing
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• v.8 no.4
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• pp.175-181
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• 2019

This paper suggests a velocity integration algorithm for Synthetic Aperture Radar (SAR) motion measurement to reduce discontinuity of range error. When using position data from Embedded GPS/INS (EGI) to form SAR image, the discontinuity of the data degrades SAR image quality. In this paper, to reduce the discontinuity of EGI position data, EGI velocity integration is suggested which obtains navigation solution by integrating velocity data from EGI. Simulation shows that the method improves SAR image quality by reducing the discontinuity of range error. INS is a similar algorithm to EGI velocity integration in the way that it also obtains navigation solution by integrating velocity measured by IMU. Comparing INS and EGI velocity integration according to grades of IMU and GPS, EGI velocity integration is more suitable for the real system. Through this, EGI velocity integration is suggested, which improves SAR image quality more than existing algorithms.

• Computers and Concrete
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• v.1 no.1
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• pp.61-76
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• 2004

The paper is devoted to present the Continuum Strong Discontinuity Approach (CSDA) and to examine its capabilities for modeling cracking of concrete. After introducing the main ingredients of the CSDA, an isotropic continuum damage model, which distinguishes tension and compression states, is used to implicitly induce a projected traction separation-law that rules the cracking phenomena. Criteria for onset and propagation of material failure and specific finite elements with embedded discontinuities are also briefly sketched. Finally, some representative numerical simulations of cracking, in plain and reinforced concrete specimens, using the CSDA are presented.

• 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.