Modeling complex crack problems using the numerical manifold method

Abstract

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.

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

“…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.…”

Influence of the geometry of partially-spanning joints on mechanical properties of rock in uniaxial compression

“…More recently, Wong (2012, 2013) studied the cracking and coalescence behavior in a rectangular rock-like specimen containing two parallel pre-existing open flaws under uniaxial compression load using a parallel bonded-particle model. Ma et al (2009) andZhang et al (2010) modeled complex crack propagation using the numerical manifold method. Wong (2012, 2013) studied the effects of the friction and cohesion on the crack growth from a closed flaw under compression using numerical manifold method.…”

Steady heat transfer analysis of 2D plates using the numerical manifold method

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