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Abstract The extended finite element method is a numerical method for modeling discontinuities within the classical finite element framework. This method can treat arbitrary cracks independent of the mesh and crack growth with minimal remeshing. Based on the principle of virtual work equation, and combined with the nonlinear complementary for contact conditions and the extended finite element discrete technique, a nonlinear complementary model for frictional contact crack problem with the extended finite element method is presented. First, the conditions that describe frictional contact are formulated as a system of non-smooth equations based on variational inequality theory, and the non-smooth damped newton method is given based on the definitions of generalized derivative to directly solve the system of equations without any extra parameters and iteration. Then, take the finite plane with a single inclined crack, edge-cracked plate as examples. The stress intensity factor of finite plane with closed crack was calculated by the interaction integral approach. The numerical solution calculated by the extended finite element method is basically consistent with the theory solution. Finally, the propagation of inclined crack under uniaxial compression is simulated by the extended finite element method. The calculation result shows that the numerical result is agreement with the experimental result and this method can accurately simulate the crack growth under uniaxial compression. Numerical example is presented to demonstrate the correctness and effectiveness of this method.
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Received: 02 July 2019
Published: 14 April 2020
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2020, Vol. 41 
