Fluid-membrane interaction based on the material point method

Abstract

SUMMARYThe material point method (MPM) uses unconnected, Lagrangian, material points to discretize solids, #uids or membranes. All variables in the solution of the continuum equations are associated with these points; so, for example, they carry mass, velocity, stress and strain. A background Eulerian mesh is used to solve the momentum equation. Data mapped from the material points are used to initialize variables on the background mesh. In the case of multiple materials, the stress from each material contributes to forces at nearby mesh points, so the solution of the momentum equation includes all materials. The mesh solution then updates the material point values. This simple algorithm treats all materials in a uniform way, avoids complicated mesh construction and automatically applies a noslip contact algorithm at no additional cost. Several examples are used to demonstrate the method, including simulation of a pressurized membrane and the impact of a probe with a pre-in#ated airbag.

Comparison study of MPM and SPH in modeling hypervelocity impact problems

“…York et al [59] simulated shock tube problem by using MPM. Oscillation, which might be caused by cell crossing noise, was observed in their results.…”

A computational strategy for simulating heat transfer and flow past deformable objects

“…The Material Point Method (MPM) [40,41,50,51] is used for solving the governing equations for the solid structure (Eq. (4) and (5)).…”

“…In all the notations we will use here, the subscript s will denote material points and the subscript i (j) will represent the background grid nodes. The momentum equation (5) on the background grid (weak form) is given by [41] …”

“…In contrast to these studies, the material point method (MPM) [40] has certain advantage over standard FEM including the ability to handle large structural deformations. While the MPM has been demonstrated in a number of studies to be an effective strategy for solid objects, its use in resolving FSI is limited to that of York et al [41] who utilized an MPM approach both the fluid and solid.…”

“…Our method combines HCIB method [37] to resolve the flow around a body with complex shape and MPM [41] to solve for the deformation of the solid structure moving under forces from the surrounding fluid. Instead of HCIBM which uses a Cartesian grid, we use the term HIBM to emphasize that we have realized this method in general curvilinear grid [42,43].…”