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1

Mode I crack problems by coupled fractal finite element and meshfree method

Rao B. N., Rajesh K. N.

Computer Assisted Mechanics and Engineering Sciences

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2010

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Vol. 17, no. 2-3-4

113-135

EN

This paper presents a coupling technique for integrating the fractal finite element method (FFEM) with element-free Galerkin method (EFGM) for analyzing homogeneous, isotropic, and two-dimensional linear-elastic cracked structures subjected to Mode I loading condition. FFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus ensuring convergence of the proposed coupled FFEM-EFGM. The proposed method combines the best features of FFEM and EFGM, in the sense that no structured mesh or special enriched basis functions are necessary and no post-processing (employing any path-independent integrals) is needed to determine fracture parameters such as stress-intensity factors (SIFs) and T-stress. The numerical results show that SIFs and T-stress obtained using the proposed method, are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack-length to width ratio, on the quality of the numerical solutions.

2

Shape sensitivity analysis of elastic shells with cracs

Taroco E., Feijoo R. A.

Journal of Theoretical and Applied Mechanics

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2003

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Vol. 41 nr 3

643-673

EN

This study concerns the application of shape sensitivity analysis as a systematic methodology to determine the energy release rate of cracked shells, within the framework of a linear elastic approach that takes into account the effect of transverse shear deformation. This methodology and the direct method of shape sensitivity analysis is applied to shells with an arbitrary middle surface and leads to an explicit general expression for the shape sensitivity of the total potential strain energy. In elastic shells with cracks, crack initiation is simulated by a change of shape characterized by a suitable tangential velocity distribution over the middle surface of the shell. In this case, a useful expression of energy release rate is expressed in terms of the strain-stress state and the adopted shape change velocity field. Finally, shape sensitivity analysis is applied to the circular cylindrical shell and thus the condition of null divergence of the corresponding Eshelby tensor is verified.

PL

Badania opisane w pracy dotyczą zastosowania analizy wrażliwości kształtu jako systematycznej metodologii wyznaczania tempa uwalnianej energii powłok z pęknięciami w ramach liniowego podejścia uwzględniającego efekt deformacji od ścinania poprzecznego. Ta metodologia i bezpośrednia analiza wrażliwości kształtu została zastosowana do powłok o dowolnej powierzchni środkowej, pozwalając na znalezienie jawnego i ogólnego wyrażenia na pochodną całkowitej energii odkształcenia. W podatnych powłokach z pęknięciami symulację inicjacji pęknięcia dokonano na podstawie zmiany kształtu określonej odpowiednim rozkładem prędkości powierzchni środkowej powłoki. W takim przypadku użyteczną formułę określającą tempo uwalnianej energii wyznaczono w funkcji stanu naprężenia i odkształcenia oraz zmian rozkładu pola prędkości powierzchni środkowej. Na koniec, analizę wrażliwości kształtu zastosowano do szczególnego przypadku powłoki cylindrycznej, gdzie warunek zerowej dywergencji odpowiadającego tensora Eshelby'ego został potwierdzony.

3

Tortuous cracks under remote mode I: the statistical LEFM approach

Pokluda J.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2001

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z. 67

277-296

EN

Principles of the statistical approach to the stability of microtortuous cracks under the remote mode I loading are presented within the framework of linear elastic fracture mechanics. The basic idea of this approach lies in the suggestion that branching occurs only at those sites along the crack front, where the characteristic structural parameter (grain size, interparticle distance) is comparable to or larger than the plastic zone size. By using procedures introduced in the paper, extrinsic contribution to the fracture toughness or to the fatigue threshold can be separated from experimentally obtained KIc or [delta]Kth values. Consequently, it enables to determine the intrinsic resistance against crack initiation and growth as a more relevant measure of materials quality. Moreover, this theory elucidates quantitatively well some interesting phenomena observed in fracture and fatigue of metallic materials.