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| Application of smooth edge domain continuous-discontinuous cellular automaton in crack propagation |
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Abstract Aiming at the crack propagation problem of rock cracks, the strain smoothing technique is combined with the continuous-discontinuous cellular automaton method, and the smooth strain fields of the discontinuous crack penetration element and the crack tip element are constructed, and the fast adaptive smooth edge domain continuous-discontinuous cellular automaton is proposed. Using the Gaussian divergence theorem to solve the smooth strain matrix, the area integral of the element is converted into a smooth domain boundary line integral, and the calculation expression of the smooth boundary domain continuous-discontinuous cellular automaton strain matrix is deduced, and an adaptive acceleration algorithm is established in which the acceleration factor is updated synchronously with the cell update. Based on this, the optimal acceleration factor is automatically obtained with the updating, and the convergence speed is greatly improved compared with the traditional cellular automaton method. The analysis and calculation program are compiled with C++, and the multi-crack crack propagation process is simulated and compared with the conventional extended finite element method. It is found that the smooth edge domain continuous-discontinuous cellular automaton has significant advantages over the conventional finite element in the accuracy, stability and convergence of the solution.
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Received: 04 October 2022
Published: 18 April 2023
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2023, Vol. 44 
