Coupled Crack /Contact Analysis for Composite Material Containing Periodic Cracks under Periodic Rigid Punches Action
Yue-Ting Zhou; Xing Li; De-Hao Yu; and Kang Yong Lee;

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 63, No. 2, pp. 163-190, 2010
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Keywords periodic cracks, contact, periodic punches, singular integral equation, Hilbert kernel.
Abstract In this paper, a coupled crack/contact model is established for the composite material with arbitrary periodic cracks indented by periodic punches. The contact of crack faces is considered. Frictional forces are modeled to arise between the punch foundation and the composite material boundary. Kolosov-Muskhelisvili complex potentials with Hilbert kernels are constructed, which satisfy the continuity conditions of stress and displacement along the interface identically. The considered problem is reduced to a system of singular integral equations of first and second kind with Hilbert kernels. Bounded functions are defined so that singular integral equations of Hilbert type can be transformed to Cauchy type. Numerical analyses are conducted through two examples. The presented approach allows considering various configurations of cracks and the punches foundation. Classic results can be obtained when the basic period ap(a > 0).
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