On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids

Wünsche, Michael; Zhang, Chuanzeng; García-Sánchez, F.; Sáez, Andrés; Sládek, J.; Sládek, V.

doi:10.1016/j.cma.2009.04.006

Cited by 14 publications

(4 citation statements)

References 27 publications

(51 reference statements)

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“… for the case considered will be defined later. (10) Then the integral representation of the components of the traction field can be also derived from the Somigliana identity (7):…”

Section: Methodsmentioning

confidence: 99%

“…The dynamic stress intensity factors were calculated for the linear finite length crack in infinite body under impact loading, where regular integrals were calculated numerically and singular and hypersingular integrals were integrated analytically. Comparison of two hypersingular time domain boundary element methods was done in [10]. In the paper the problem of linear crack under transient load situated in two-dimensional, homogeneous, anisotropic and linear elastic solid was considered.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effects of crack closure and friction for linear crack under normal impact

Menshykov

Menshykova

Guz

2020

Engineering Analysis with Boundary Elements

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“… for the case considered will be defined later. (10) Then the integral representation of the components of the traction field can be also derived from the Somigliana identity (7):…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effects of crack closure and friction for linear crack under normal impact

Menshykov

Menshykova

Guz

2020

Engineering Analysis with Boundary Elements

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“…Only the line integrals over the unit circle arising in the regular parts of the dynamic fundamental solutions have to be computed numerically. More details of the solution algorithm can be found in [40,41].…”

Section: Spatial and Temporal Discretizationsmentioning

confidence: 99%

Dynamic crack analysis in piezoelectric solids with non-linear electrical and mechanical boundary conditions by a time-domain BEM

Wünsche

Zhang

García-Sánchez

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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“…Although the FD formulation requires the use of Fourier/Laplace transform if time solutions are needed, its implementation is generally simpler than for the TD formulation. For BEM works on the dynamic crack-inclusion interaction, FD formulation has been employed by Mykhas'kiv and Khay [11] while TD formulation has been preferred by several other research groups (e.g., [12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

Symmetric-Galerkin Boundary Element Transient Analysis of the DSIFs for the Interaction of a Crack with a Circular Inclusion

Phan

Gray

Salvadori

2010

KEM

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A dynamic analysis of crack-inclusion interaction is described in this paper. The analysis employs a two-dimensional symmetric-Galerkin boundary integral formulation for multi-domain elastodynamic fracture analysis in the frequency domain. The multi-domain technique is based on the assumption of perfectly bonded inclusions. The numerical implementation of this boundary integral formulation is carried out with standard quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the rst part is identical to that for elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs are obtained in a post-processing step by applying the fast Fourier transform (FFT) and inverse FFT to the frequency responses of these DSIFs. Two numerical examples are presented for the computation of the DSIFs due to crack-inclusion interaction under two types of impact loading: Heaviside step loading and blast loading. The numerical results are consistent and conrm the well known crack tip shielding mechanism observed during the interaction between a crack and a much stier inclusion.

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On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids

Cited by 14 publications

References 27 publications

Effects of crack closure and friction for linear crack under normal impact

Effects of crack closure and friction for linear crack under normal impact

Dynamic crack analysis in piezoelectric solids with non-linear electrical and mechanical boundary conditions by a time-domain BEM

Symmetric-Galerkin Boundary Element Transient Analysis of the DSIFs for the Interaction of a Crack with a Circular Inclusion

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