A hypersingular time‐domain BEM for 2D dynamic crack analysis in anisotropic solids

Wünsche, Michael; Zhang, Ch.; Kuna, Meinhard; Hirose, Sohichi; Sládek, J.; Sládek, V.

doi:10.1002/nme.2477

Cited by 19 publications

(7 citation statements)

References 23 publications

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“…The development of anisotropic BEM shows that Dravinski & Wilson (2001), Dravinski (2003), Daros (2013) and Chiang (2018) concentrated on the different aspects of orthotropy effect. Moreover, Wang et al (1996), Zhang (2002), Wunsche et al (2009), Furukawa et al (2014), and Parvanova et al (2016) demonstrated the wave propagation in the anisotropic medium. Also, Zheng & Dravinski (1998, and Dineva et al (2014) investigated the scattering of seismic waves in an orthotropic half-space.…”

Section: Literature Surveymentioning

confidence: 94%

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

Mojtabazadeh-Hasanlouei

Panji

Kamalian

2023

Preprint

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A simple numeric model named DASBEM was successfully developed to analyze the seismic heterogeneous orthotropic hill-shaped topographies by a time-domain boundary element method based on half-space Green’s functions. The model was elaborated only by discretizing the hill surface and its interface with the underlying half-space in the use of image source theory and substructure approach. To improve the model at the corners, the double node procedure was applied to extreme nodes of the used quadratic elements. An attenuation ratio is implemented in the boundary equations using a decremental exponential function. After presenting the technique, a validation example presented beside the literature to measure the convergence with an isotropic response. Then, a sample Gaussian–shaped hill model is prepared under propagating obliquely incident SH-waves as common sample topography and the surface response is obtained by considering some significant parameters as well as the shape ratio, isotropy factor, frequency content, and angle of the incident wave. The ground surface response is sensitized in two time and frequency realms. The results showed that the amplitude of the response was not only dependent on the impedance ratio but also the isotropy ratio was always effective in orienting the wavefront to amplify the ground movement.

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Section: Literature Surveymentioning

confidence: 94%

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

Mojtabazadeh-Hasanlouei

Panji

Kamalian

2023

Preprint

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“…In the calculations, displacements and tractions with components u i and t i are prescribed on the grain and phase boundaries (boundary C b ), while relative displacements Du i and stresses r ia are considered in the shear band layers (faces C s ). The computation procedure is based on two boundary integral equations [21]: the displacement boundary integral equation, which is applied on the boundary C b , and the stress boundary integral equation, which is used on the faces C s .…”

Section: Methodsmentioning

confidence: 99%

Cyclic deformation behavior of austenitic Cr–Ni-steels in the VHCF regime: Part II – Microstructure-sensitive simulation

Hilgendorff

Grigorescu

Zimmermann

et al. 2016

International Journal of Fatigue

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“…The inconvenience of this approach is that the BEM formulation will now involve integrals including both strong singularities which require special treatment. Numerous hypersingular approaches have been developed, in particular to anisotropic materials under static [ 90 , 91 , 150 , 282 ] and time-harmonic [ 6 , 93 , 94 , 226 , 232 , 283 , 294 ] loadings. The use of a hypersingular formulation does not limit at all the crack shape, being valid for curved and branched cracks, for example.…”

Section: Discrete Numerical Methodsmentioning

confidence: 99%

Numerical Simulation of Fracking in Shale Rocks: Current State and Future Approaches

Hattori

Trevelyan

Augarde

et al. 2016

Arch Computat Methods Eng

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Extracting gas from shale rocks is one of the current engineering challenges but offers the prospect of cheap gas. Part of the development of an effective engineering solution for shale gas extraction in the future will be the availability of reliable and efficient methods of modelling the development of a fracture system, and the use of these models to guide operators in locating, drilling and pressurising wells. Numerous research papers have been dedicated to this problem, but the information is still incomplete, since a number of simplifications have been adopted such as the assumption of shale as an isotropic material. Recent works on shale characterisation have proved this assumption to be wrong. The anisotropy of shale depends significantly on the scale at which the problem is tackled (nano, micro or macroscale), suggesting that a multiscale model would be appropriate. Moreover, propagation of hydraulic fractures in such a complex medium can be difficult to model with current numerical discretisation methods. The crack propagation may not be unique, and crack branching can occur during the fracture extension. A number of natural fractures could exist in a shale deposit, so we are dealing with several cracks propagating at once over a considerable range of length scales. For all these reasons, the modelling of the fracking problem deserves considerable attention. The objective of this work is to present an overview of the hydraulic fracture of shale, introducing the most recent investigations concerning the anisotropy of shale rocks, then presenting some of the possible numerical methods that could be used to model the real fracking problem.

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A hypersingular time‐domain BEM for 2D dynamic crack analysis in anisotropic solids

Cited by 19 publications

References 23 publications

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

A Simple Time-Domain BEM Model for Heterogeneous Orthotropic Hill-Shaped Topographies Under Attenuated Incident SH-Wave

Cyclic deformation behavior of austenitic Cr–Ni-steels in the VHCF regime: Part II – Microstructure-sensitive simulation

Numerical Simulation of Fracking in Shale Rocks: Current State and Future Approaches

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