Efficient Runge–Kutta solver for stochastic crack growth analysis

Abstract

Stochastic crack growth analysis by simulation may easily require a significant amount of computational effort. The Initial Value ordinary differential equations appearing in crack propagation problems may be solved by the Runge–Kutta (RK) family of solvers. However, crack propagation considering uncertainties imposes additional challenges for RK solvers: possibility of vectorized and/or parallelized computation of sample realizations; and adaptation of time discretization for each sample, to handle changes and discontinuities in the derivatives of crack growth curves, caused by changes in loads and in crack propagation rates. Existing adaptive RK methods, with change in time step length during crack growth computation, struggle with these challenges. In this setting, the present paper proposes a modified adaptive RK method which allows for simultaneous crack growth computations with different time-step discretizations, and aims at efficiently dealing with cases where discontinuities are present in the derivative of the crack growth curve. Application of the proposed method to three crack propagation examples, including one related to weld flaws in pipes, indicates that it is as accurate as other adaptive methods from the literature, while requiring only a fraction of the computational time.