Fracture analysis of functionally graded materials by a BEM

Gao, Xiao‐Wei; Zhang, Ch.; Sládek, J.; Sládek, V.

doi:10.1016/j.compscitech.2007.08.029

Cited by 98 publications

(34 citation statements)

References 41 publications

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“…Due to the dimension-reduction, the remeshing procedure is fairly simple as the crack is part of the boundary. Interesting applications of the BEM to fracture can be found, for example, in [240][241][242][243][244][245][246][247][248][249][250][251][252][253][254][255][256][257].…”

Section: Boundary Element Methodmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

161

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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Section: Boundary Element Methodmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

161

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“…Green functions of the exponentially graded media have been derived using Fourier transform techniques. Furthermore, crack analysis of the 2D continuous and linear elastic FGMs has been accomplished by Yue et al (2003) and Gao et al (2008).…”

Section: Introductionmentioning

confidence: 99%

A time-domain boundary element method for quasistatic thermoviscoelastic behavior modeling of the functionally graded materials

Ashrafi

Shariyat

Asemi

2013

Int J Mech Mater Des

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In the present paper, a boundary element formulation is presented for two-dimensional thermoviscoelasticity analysis of components fabricated from the functionally graded materials (FGMs). In this regard, a graded viscoelastic element capable of tracing gradual variations of the material properties is developed. Several attempts have been made so far to employ the integral equation approach for the heterogeneous viscoelastic materials. In the present research, Somigliana's displacement identity is considered and implemented numerically for analyzing the two-dimensional exponentially graded viscoelastic components. Employing the common assumptions of the viscoelastic constitutive equations and the weighted residual technique, an efficient boundary element formulation is developed for the heterogeneous Kelvin-Voigt solid viscoelastic models. Finally, three numerical examples are provided to verify the proposed formulation and present practical conclusions.

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“…Using a Fourier transform technique, these functions have been derived for exponentially graded media. Although extensive works have been developed to effectively model the constitutive behavior of the FG structures, most of these researches have been limited to elastic behavior analysis (Gao et al 2008;Wang and Qin 2012;Ashrafi et al 2013aAshrafi et al , 2013b.…”

Section: Introductionmentioning

confidence: 99%

A numerical boundary integral equation analysis for standard linear viscoelastic media made of functionally graded materials

Ashrafi

Shariyat

2014

Int J Mech Mater Eng

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Background: Although structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures. Methods: In the present paper, a 2D boundary element formulation capable of modeling time-dependent functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity in terms of the displacements is developed to solve 2D problems of the exponentially graded viscoelasticity. The FGM concept can be applied to various materials, for structural and functional purposes. In this model, only Green functions of the nonhomogeneous elastostatic problems are needed with material properties that vary continuously along a given dimension. Results and Conclusions: Results reveal that the boundary element approach can successfully be employed for the present complicated problem for arbitrary time histories of the applied loads and arbitrary boundary conditions, without the need to use relaxation functions or mathematical transformations.

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Fracture analysis of functionally graded materials by a BEM

Cited by 98 publications

References 41 publications

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

A time-domain boundary element method for quasistatic thermoviscoelastic behavior modeling of the functionally graded materials

A numerical boundary integral equation analysis for standard linear viscoelastic media made of functionally graded materials

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