• 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.

• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.411-427
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• 1995

The most known continuum damage theories for brittle structures are suitable to model the degradation of the material due to the deformation process and the consequent initiation of a macro-crack. Nevertheless, they are not able to describe the propagation of the crack that leads, eventually, to the breakage of the structure into parts that undergo rigid body motion. This paper presents a theory, formulated from formal arguments of Continuum Mechanics, that may describe not only the degradation but also the fracture of elastic structures. The modeling of such a discontinuous phenomenon through a continuous theory is possible by taking a cohesion variable, related with the links between material points, as an additional degree of kinematical freedom. The possibilities of the proposed theory are discussed through examples.

• Computers and Concrete
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• v.1 no.2
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• pp.131-150
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• 2004

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

• Structural Engineering and Mechanics
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• v.67 no.1
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• pp.79-85
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• 2018

Topology optimization of steel and concrete composite based on truss-like material model is studied in this paper. First, the initial design domain is filled with concrete, and the steel is distributed in it. The problem of topology optimization is to minimize the volume of steel material and solved by full stress method. Then the optimized steel and concrete composite truss-like continuum is obtained. Finally, the distribution of steel material is determined based on the optimized truss-like continuum. Several numerical results indicate the numerical instability and rough boundary are settled. And more details of manufacture and construction can be presented based on the truss-like material model. Hence, the truss-like material model of steel and concrete is efficient to establish the distribution of steel material in concrete.

• Structural Engineering and Mechanics
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• v.53 no.1
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• pp.105-130
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• 2015

In this paper, the classical continuum mechanics is adopted and modified to be consistent with the unique behavior of micro/nano solids. At first, some kinematical principles are discussed to illustrate the effect of the discrete nature of the microstructure of micro/nano solids. The fundamental equations and relations of the modified couple stress theory are derived to illustrate the microstructural effects on nanostructures. Moreover, the effect of the material surface energy is incorporated into the modified continuum theory. Due to the reduced coordination of the surface atoms a residual stress field, namely surface pretension, is generated in the bulk structure of the continuum. The essential kinematical and kinetically relations of nano-continuums are derived and discussed. These essential relations are used to derive a size-dependent model for Mindlin functionally graded (FG) nano-plates. An analytical solution is derived to show the feasibility of the proposed size-dependent model. A parametric study is provided to express the effect of surface parameters and the effect of the microstructure couple stress on the bending behavior of a simply supported FG nano plate.

• Journal for History of Mathematics
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• v.33 no.6
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• pp.327-343
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• 2020

This study investigate philosophical discussions related to the Zeno's paradoxes in order to derive the mathematics educational implications. The paradox of Zeno's motion is sometimes explained by the calculus theories. However, various philosophical discussions show that the resolution of Zeno's paradox by calculus is not a real solution, and the concept of a continuum which is composed of points and the real number continuum may not coincide with the physical space and time. This is supported by the fact that the hyperreal number system of nonstandard analysis could be another model of a straight line or time and that an alternative explanation of Zeno's paradox was possible by the hyperreal number system. The existence of two different theories of the continuum suggests that teachers and students may not have the same view of the continuum. It is also suggested that the real world model used in school mathematics may not necessarily match the student's intuition or mathematical practice, and that the real world application of mathematics theory should be emphasized in education as a kind of 'correspondence.'

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.279-301
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• 2008

This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

• Journal of Korean Society of Archives and Records Management
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• v.21 no.3
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• pp.1-16
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• 2021

Record continuum is a theory providing the basis for archival science in the paradigm shift to the electronic record environment. However, critical analysis of it has been hardly performed so far, as it is still in development, and its core is a new perspective on records different from the life cycle model. Therefore, for further understanding of the significance and limitations of record continuum in the electronic record environment and performance of more in-depth theoretical development, an analysis of the meaning and nature of records contained in record continuum logic is essential. Given that record continuum does not define a record separately, the meaning and nature of records it contains in the recent electronic record environment are examined through the analysis of axis and dimension in a record continuum model.

• Tunnel and Underground Space
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• v.29 no.5
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• pp.318-331
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• 2019

A three-dimensional(3D) equivalent continuum modeling was performed to analyze hydraulic behavior of rock mass considering discontinuities by using DFN model and smeared fracture model. DFN model was generated by FLAC3D and smeared fracture model was applied by using FISH functions, which is built-in functions in FLAC3D, for equivalent continuum model of fractured rock mass. Comparative analysis with 3DEC, which is for discontinuum analysis, was conducted to verify reliability of equivalent continuum analysis by using FLAC3D. Similar results of hydraulic analysis under the same conditions could be achieved. Equivalent continuum analysis of fractured rock mass by using DFN model was implemented to compare with existing analytical methods for inflow into the tunnel.

• Journal of Theoretical and Applied Mechanics
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• v.2 no.1
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• pp.31-50
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• 1996

In this paper, a finite element analysis based on the local approach concept to fracture in the continuum damage mechanics is performed to analyze ductile fracture in two dimensional quasi-static state. First an isotropic damage model based on the generalized concept of effective stress is proposed for structural materials in the context of large deformation. In this model, the stiffness degradation is taken as a measure of damage and so, the fracture phenomenon can be explained as the critical deterioration of stiffness at a material point. The modified Riks' continuation technique is used to solve incremental iterative equations. Crack propagation is achieved by removing critically damaged elements. The mesh size sensitivity analysis and the simulation of the well known shearing mode failure in plane strain state are carried out to verify the present formulation. As numerical examples, an edge cracked plate and the specimen with a circular hole under plane stress are taken. Load-displacement curves and successively fractured shapes are shown. From the results, it can be concluded that the proposed model based on the local approach concept in the continuum damage mechanics may be stated as a reasonable tool to explain ductile fracture initiation and crack propagation.