Modeling complex crack problems using the numerical manifold method |
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Authors: | G W Ma X M An H H Zhang L X Li |
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Affiliation: | (1) School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore;(2) MOE Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, 710049 Xi’an, Shaanxi, People’s Republic of China |
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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. |
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Keywords: | Numerical manifold method Mathematical cover Physical cover Weight function Cover function Complex crack problems |
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