In this paper, an inertia-based stabilizing method is proposed to overcome the loss of numerical convergence in quasi-static simulations of fracture problems with unstable (fast or dynamic) crack propagation. The method guarantees unconditional convergence as the time increment step progressively decreases and it does not need any numerical damping or other solution enhancement parameters. It has been demonstrated, through direct simulations of several numerical examples with severe local or global instabilities, that the proposed method can effectively and efficiently overcome severe instability points unconditionally and regain stability if there exist mechanisms for stable crack propagation after passing through such instability points. In all the numerical tests, the new method outperforms other solution enhancement techniques, such as numerical damping, arc-length method, and implicit dynamic simulation method, in the solution accuracy and numerical robustness.

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