Micromechanical elastic cracktip stresses in a fibrous composite

Fish, Jacob; Fares, Nabil; Nath, Aditya

doi:10.1007/bf00012441

Cited by 14 publications

(7 citation statements)

References 14 publications

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Section: Generalities About Global/local Analysismentioning

confidence: 99%

“…In [7] such an approach was employed in order to resolve crack-tip fields in fibrous composites. This technique which in [7] is called the mesh-superposition method may be described as follows: A composite plate, which may include cracks, is first analyzed as a homogeneous orthotropic continuum using a finite element mesh which is called the macro-mesh. The local behavior on the scale of the heterogeneous constituents is then analyzed using a separate finite-element mesh called the micro-mesh which employs elements which are small enough to reflect the micro variations in material behavior and is superimposed on the macro-mesh in the neighborhoods of the crack-tips where the critical behavior is expected.…”

Section: Generalities About Global/local Analysismentioning

confidence: 99%

See 1 more Smart Citation

Pollution Error in the h-Version of the Finite Element Method and the Local Quality of A-Posteriori Error Estimators

Babuska¹,

Strouboulis²,

Upadhyay³

et al. 1994

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Section: Generalities About Global/local Analysismentioning

confidence: 99%

Section: Generalities About Global/local Analysismentioning

confidence: 99%

Pollution Error in the h-Version of the Finite Element Method and the Local Quality of A-Posteriori Error Estimators

Babuska¹,

Strouboulis²,

Upadhyay³

et al. 1994

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“…Among the noteworthy SGEMs are the s-version of the finite element method [19,20,21,22] with application to strong [23,24] and weak [25,26,27,28] discontinuities, various multigrid-like scale bridging methods [29,30,31,32], the Extended Finite Element Method (XFEM) [33,34,35] and the Generalized Finite Element Method (GFEM) [36,37] both based on the Partition of Unity (PU) framework [38,39] and the Discontinuous Galerkin (DG) [40,41] method. Multiscale methods based on the concurrent resolution of multiple scales are often called as embedded, concurrent, integrated or hand-shaking multiscale methods.…”

Section: Introductionmentioning

confidence: 99%

Multiscale enrichment based on partition of unity

Fish¹,

Yuan²

2004

Numerical Meth Engineering

139

110

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A new Multiscale Enrichment method based on the Partition of Unity (MEPU) method is presented. It is a synthesis of mathematical homogenization theory and the Partition of Unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. MEPU is perfectly suited for enriching the coarse scale continuum descriptions (PDEs) with fine scale features and the quasi-continuum formulations with relevant atomistic data. Numerical results show that it provides a considerable improvement over classical mathematical homogenization theory and quasi-continuum formulations.

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“…A composite plate of fiber-matrix is modeled by global mesh and a local mesh for micro crack. The material properties for global are calculated by mixture rule [25].…”

Section: Global-local Approach For Concurrent Multiscale Analysismentioning

confidence: 99%

Recent research progress in computational solid mechanics

Zhuang

Maitireyimu

2012

Chin. Sci. Bull.

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Computational mechanics has had a profound impact on science and technology over the past five decades. It has numerically transformed much of the classical theory models into practical tools for predicting and understanding the complex engineering and science system. A short review is given in this paper on some recent progress in computational solid mechanics at multi-scales.computational solid mechanics, extended finite element method, molecule dynamic, multi-scales Citation:Zhuang Z, Maitireyium M. Recent research progress in computational solid mechanics. Chin Sci Bull, 2012Bull, , 57: 46834688, doi: 10.1007 Computational mechanics has had a profound impact on science and technology over the past five decades. It has numerically transformed much of the classical Newtonian theory into practical tools for predicting and understanding the complex engineering and science system, which have some limitations using the classic analytical solutions. Finite element methodology (FEM), which is one of the most powerful computation tools, has been widely used in the simulation-based engineering and science. There are a number of methods based on FEM dealing with the problem of material behaviors and structural mechanics, for example, damage and fracture. Since the limitation of FEM is in the continuum problem ranging from micro-meter to macro scales, the molecule dynamic (MD) computation is used at nano-scale research. A short review is given in this paper on the recent progress in computational solid mechanics related to length scales. MD simulation at nano-scaleThe carbon nano-tube (CNT) as a representative nano-scale material was invented twenty years ago. Its material behavior and mechanics has been interested by many researchers and engineers. The investigations were carried out from the aspects of theory, experiment and simulation. Since it is discrete at atomic length, the MD method is the best tool in the numerical analysis. Another purpose using MD simulation is to provide the failure criterion for dislocation initiation in the crystals, which can link the scales from nano-meter to micron. The minimum energy principle for the dislocation nucleation or initiation was predicted for inhomogeneous atomic system [1]. The simulation results illustrated that the thin film is easily nucleated on the surface because the atomic bonds lose. Based on MD simulation at nano-size and theoretical analysis, an investigation of the combined size and rate effects on the mechanical responses of faced cubic crystal (FCC) metals has been made to develop a hyper-surface (Figure 1) crossing the length scales [2]. The high strength and hard toughness properties of crystalline solid were intensively investigated at sub-micron and nanoscales. In these scales, the forms of defects in a crystal material are dislocation and grain boundary. A majority of research papers were focused on the dislocation nucleation and the interactions between dislocation and grain boundary [3]. The yield strength of perfect crystal depends on dislocation nu...

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Micromechanical elastic cracktip stresses in a fibrous composite

Cited by 14 publications

References 14 publications

Pollution Error in the h-Version of the Finite Element Method and the Local Quality of A-Posteriori Error Estimators

Pollution Error in the h-Version of the Finite Element Method and the Local Quality of A-Posteriori Error Estimators

Multiscale enrichment based on partition of unity

Recent research progress in computational solid mechanics

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