Modeling irregular boundaries using isoparametric elements in the Material Point Method

TL;DR

This paper introduces a method using unstructured isoparametric elements within the Material Point Method to accurately model irregular boundaries, validated through simulations of landslides and debris flows.

Contribution

It proposes an inverse mapping algorithm with unstructured meshes for boundary modeling in MPM, enhancing the simulation of complex, evolving boundaries.

Findings

Successfully modeled landslide topography and debris flow dynamics.

Validated approach against USGS flume test data.

Improved boundary representation in large deformation simulations.

Abstract

The Material Point Method (MPM) is a hybrid Eulerian-Lagrangian approach capable of simulating large deformation problems of history-dependent materials. While the MPM can represent complex and evolving material domains by using Lagrangian points, boundary conditions are often applied to the Eulerian nodes of the background mesh nodes. Hence, the use of a structured mesh may become prohibitively restrictive for modeling complex boundaries such as a landslide topography. We study the suitability of unstructured background mesh with isoparametric elements to model irregular boundaries in the MPM. An inverse mapping algorithm is used to transform the material points from the global coordinates to the local natural coordinates. Dirichlet velocity and frictional boundary conditions are applied in the local coordinate system at each boundary node. This approach of modeling complex boundary conditions is validated by modeling the dynamics of a gravity-driven rigid block sliding on an inclined plane. This method is later applied to a flume test of controlled debris flow on an inclined plane conducted by the United States Geological Survey (USGS).