Material Point Method (MPM) Analysis of Hydrodynamic Impact Problems Involving Embedded Solids

Abstract

Impact of debris carried by floods or tsunamis can cause severe damage to bridges, though they are not well studied in the literature. The Material Point Method (MPM) provides a framework for modeling such systems involving combined fluid/solid behavior with complex interactions. Conventional MPM uses regular grids with tri-linear interpolation. However, linear functions introduce volumetric locking for (nearly) incompressible materials, posing problems when modeling fluids. To eliminate locking, nodebased, cellbased and hybrid formulations were adapted by Mast et al., J. Comp. Phys., Vol. 231, pp 5351–5373, (2012). In this paper we propose a new numerical flux smoothing algorithm to produce smooth stress fields in complex hydrodynamic problems while ensuring numerical stability. The goal is not only to produce strain and stress fields free of locking, but also to stabilize high frequency numeric oscillation. The improved algorithms are applied to fluid driven debris impact problems, and validated against experimental results. Emphasis is in given to evaluating demands on bridge superstructures by tsunami driven debris.