Crack Growth Prediction by Manifold Method

Tsay, Ren-Jow; Chiou, Yaw‐Jeng; Chuang, W. Y.

doi:10.1061/(asce)0733-9399(1999)125:8(884)

Cited by 107 publications

(31 citation statements)

References 15 publications

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“…The NMM has been used to investigate discontinuous problems involving stationary cracks and crack propagation (Tsay et al 1999), and extended by various researchers to address crack problems (Li et al 2005;Ma et al 2009;Zhang et al 2010a;Wong 2012, 2013) and failure of rock slopes involving cracking (Zhang et al 2010b;Ning et al 2011;Wong and Wu 2014). However, the tips of cracks are constrained to stop at the edges of the element, which reduces the accuracy if a crack tip happens to stop inside an element when the NMM is used to investigate discontinuous problems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Zhou

2014

Rock Mech Rock Eng

306

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A novel meshless numerical method, called general particle dynamics (GPD), is proposed to simulate samples of rock-like brittle heterogeneous material containing four preexisting flaws under uniaxial compressive loads. Numerical simulations are conducted to investigate the initiation, growth, and coalescence of cracks using a GPD code. An elasto-brittle damage model based on an extension of the Hoek-Brown strength criterion is applied to reflect crack initiation, growth, and coalescence and the macrofailure of the rock-like material. The preexisting flaws are simulated by empty particles. The particle is killed when its stresses satisfy the Hoek-Brown strength criterion, and the growth path of cracks is captured through the sequence of such damaged particles. A statistical approach is applied to model the heterogeneity of the rocklike material. It is found from the numerical results that samples containing four preexisting flaws may produce five types of cracks at or near the tips of preexisting flaws including wing, coplanar or quasi-coplanar secondary, oblique secondary, out-of-plane tensile, and out-of-plane shear cracks. Four coalescence modes are observed from the numerical results: tensile (T), compression (C), shear (S), and mixed tension/shear (TS). A higher load is required to induce crack coalescence in the shear mode (S) than the tensile (T) or mixed (TS) mode. It is concluded from the numerical results that crack coalescence occurs following the weakest coalescence path among all possible paths between any two flaws. The numerical results are in good agreement with reported experimental observations.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Zhou

2014

Rock Mech Rock Eng

306

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“…Based on the two-cover procedure, this method can be used to solve problems dealing with both continuum and discontinuities in a unified framework. The methods related to NMM have been successfully applied to the prediction of the growth of cracks, the failure simulation of slope, linear and non-linear analysis for heterogeneous solids [3][4][5]. On the other hand, the study on developing numerical manifold element (NME) is still going on in recent years.…”

Section: Introductionmentioning

confidence: 99%

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

Zhang

Zhou

2006

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYIt is well known that the Babuska-Brezzi stability criterion or the Zienkiewicz-Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u-p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second-order displacement and the first-order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed.

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“…The advantages of the NMM lie in solving discontinuous problems, and simple crack problems have been modeled by Tsay et al (1999), Chiou et al (2002) and Li et al (2005). This paper intends to exhibit the capability of the NMM in modeling complex crack problems such as multiple intersecting cracks and branched cracks, as compared with other effective methods such as the XFEM and the GFEM.…”

Section: Introductionmentioning

confidence: 98%

Modeling complex crack problems using the numerical manifold method

Zhang

et al. 2009

Int J Fract

230

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In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the physical domain, over which cover functions with unknowns to be determined are defined. With these two kinds of covers, the method is quite suitable for modeling discontinuous problems. In this paper, complex crack problems such as multiple branched and intersecting cracks are studied to exhibit the advantageous features of the numerical manifold method. Complex displacement discontinuities across crack surfaces are modeled by different cover functions in a natural and straightforward manner. For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems.

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Crack Growth Prediction by Manifold Method

Cited by 107 publications

References 15 publications

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

Modeling complex crack problems using the numerical manifold method

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