Spherically-symmetric form of the material point method with applications to underwater explosion

In solving the shock response problems of three-dimensional far-field underwater explosion by the material point method, the calculation of the propagation process of the shock wave before it reaches the structure will cost a large amount of computing resources and affect the computing efficiency. Aimed to this problem, a one-dimensional spherically-symmetric form of the material point method was proposed by taking into account the propagation characteristics of the underwater explosion shock waves in the free field. And the underwater explosion of the spherical explosive was numerically simulated by the proposed material point method. The simulated results are in good agreement with the ones obtained by the Cole formula and DYNA, and it can explain that the proposed material point method is feasible. On the basis of the above results, a re-mapping algorithm was brought forward based on the material point method. The blast wave propagation in the free field was calculated in the one-dimensional spherically-symmetric model, and the calculated results were mapped to the three-dimensional model to complete the calculation process. So the computation efficiency is improved greatly.