Crack analyses in porous piezoelectric brittle materials by the SBFEM

Sládek, J.; Sládek, V.; Krahulec, Slavomír; Song, Chongmin

doi:10.1016/j.engfracmech.2016.03.046

Cited by 20 publications

(8 citation statements)

References 22 publications

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“…It is known for its robust applications in problems of unbounded media() and fracture. () In the former, the SBFEM can analytically model the radiation boundary condition at infinity and leads to a rational representation of the radiation damping. In the latter, the asymptotic stress singularities of any kind can be analytically modelled without fine crack tip meshes or special techniques in the vicinity of stress concentrators.…”

Section: Scaled Boundary Femmentioning

confidence: 99%

A scaled boundary finite element formulation for poroelasticity

Ooi

Song

Natarajan

2018

Numerical Meth Engineering

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Summary This paper develops the scaled boundary finite element formulation for applications in coupled field problems, in particular, to poroelasticity. The salient feature of this formulation is that it can be applied over arbitrary polygons and/or quadtree decomposition, which is widely employed to traverse between small and large scales. Moreover, the formulation can treat singularities of any order. Within this framework, 2 sets of semianalytical, scaled boundary shape functions are used to interpolate the displacement and the pore fluid pressure. These shape functions are obtained from the solution of vector and scalar Laplacian, respectively, which are then used to discretise the unknown field variables similar to that of the finite element method. The resulting system of equations are similar in form as that obtained using standard procedures such as the finite element method and, hence, solved using the standard procedures. The formulation is validated using several numerical benchmarks to demonstrate its accuracy and convergence properties.

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Section: Scaled Boundary Femmentioning

confidence: 99%

A scaled boundary finite element formulation for poroelasticity

Ooi

Song

Natarajan

2018

Numerical Meth Engineering

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“…Але розв'язання просторових задач електропружності пов'язане зі значними труднощами математичного характеру, оскільки основна система рівнянь електропружності є зв'язаною стосовно силових і електричних полів системою диференціальних рівнянь у частинних похідних [1,4], розв'язок якої отримати набагато важче, ніж розв'язок чисто пружної задачі. Тому на цей час з більшою повнотою вивчено простіші дво-вимірні задачі електропружності, серед яких можна вирізнити праці [11,13,14,23,27], присвячені дослідженню електропружного стану як поблизу одиночних порожнин, включень, тріщин, так і у взаємодії кількох концентраторів електричних і механічних полів. У працях [5,24] запропоновано методологічно подібні підходи до побудови загальних розв'язків зв'язаної системи тривимірних статичних рівнянь електропружності для трансверсальноізотропних тіл, за допомогою яких отримано точні розв'язки низки задач електропружності за спеціальної орієнтації концентратора напружень відносно осі симетрії трансверсально-ізотропного електропружного матеріалу.…”

Section: вступunclassified

Mathematical modeling of the electrostressed state in the orthotropic piezoelectric space with an arbitrary orientated circle crack under uniaxial tension

Kirilyuk¹,

Levchuk²

2018

SRIT

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“…The generalised stress intensity factors can be determined directly from the scaled boundary finite element solution by following a standard stress recovery procedure. This method has also been extended to model piezoelectric materials [52,53,54]. The semi-analytical solution of stress field is convenient to use in the finite fracture mechanics [55].…”

Section: Introductionmentioning

confidence: 99%

A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

Song

Ooi

Natarajan

2018

Engineering Fracture Mechanics

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145

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The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semianalytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygonal elements in geometric shape leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility.

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Crack analyses in porous piezoelectric brittle materials by the SBFEM

Cited by 20 publications

References 22 publications

A scaled boundary finite element formulation for poroelasticity

A scaled boundary finite element formulation for poroelasticity

Mathematical modeling of the electrostressed state in the orthotropic piezoelectric space with an arbitrary orientated circle crack under uniaxial tension

A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

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