The long-range interaction between one incompressible fluid surrounding solid objects is quite common and includes suspensions, sedimentation, fluid motion around obstacles, and erosion. Concerning the active research field of fluid-solid interactions, the challenging point nowadays is to describe the fluid dynamics in the pore space of soils or concrete samples and to establish a full coupling between the fluid and the movable deformable solid phase. This paper describes an extension of the material-point method (MPM) to modelling the interactions of incompressible fluids and multi-body deformable particles, which are discretized by a collection of unconnected, Lagrangian, material points. Primary variables, such as displacement, velocity, pressure and acceleration, and material variables, such as mass, stress and strain are associated with these points. To solve the equations of motion, data mapped from the material points are used to update variables on a background Eulerian mesh. The mesh solution is then mapped back to material points. This standard particle-like method treats all materials in a uniform way, thus avoiding complicated mesh construction and automatically possessing a no-slip contact algorithm at no additional cost.

In this study, the solid phase is treated as elastic, but general in-
elastic descriptions can also be later included to explore the interaction
with the fluid phase. On the other hand, problems of incompressibility
introduce numerical difficulties which need to be treated.  Hence the
enhanced strain method is adapted to the MPM analysis and spec-
ified to the study of long-range hydrodynamic interactions between
incompressible fluid and solid deformable objects.  Numerical exam-
ples including a fluid flow around an obstacle, the collapse of a water
column and a sedimentation test are used to illustrate the proposed
approach and its potential.   The results of the MPM are compared
with those obtained with classical FEM, XFEM and a modified im-
mersed boundary method. In addition, the MPM results also compare
well with existing experimental measurements of the collapsing water
problem.