Accelerating convergence of crack propagation simulation in peridynamic models via high-order temporal discretization

This work proposes a high-order temporal discretization for reformulations of both bond-based and state-based peridynamic models modeling, e.g. crack propagation. It is discovered from various experiments that for such discontinuous problems, commonly-used second-order methods are less stable and more computationally consuming than the high-order method, which indicates that the high-order temporal discretization not only improves the accuracy and the efficiency for conventional smooth problems, but also exhibits a promising behavior for some non-smooth models such as peridynamics.