An adaptive coupling of finite elements with smooth particle hydrodynamics particles for large deformation fluid–solid interactions

Abstract

This article presents a simple technique to couple the finite element method (FEM) and the smooth particle hydrodynamics (SPH) method in the Lagrangian framework for the simulation of problems involving solids and structures under shock loading that cause large deformations, such as rock blasting. For such problems FEM suffers from mesh distortion and thus requires some numerical corrective measures such as element erosion or remeshing to proceed with the solution. These cause some artificial effects and a sufficient increase in the computational time. Mesh-less particle based methods such as SPH, on the other hand offer the flexibility to handle high-speed motion inherently. But the SPH method is more computationally demanding and requires special treatment for application of boundary conditions. For the simulation of certain process that involve high impact by fluid on solids or structures such as blasting, a coupled FEM-SPH procedure might be more efficient where regions of large deformations are modeled with SPH particles and regions far off are modeled with FEM. An adaptive procedure of coupling FEM-SPH is developed in this work so that highly distorted elements in the model are replaced by SPH particles on the fly but remain linked to the model thus maintaining the consistency in solution. The article provides the details of this adaptive procedure. Validation of this coupling method is done by analyzing a two-dimensional (2D) elastic impact problem and then is applied for the 2D simulation of fragmentation in brittle rocks induced by high impact blast loads from explosions considering a continuum damage model under plain strain conditions. Since detailed three-dimensional (3D) FSI simulations require, even for the lone SPH or FEM solver, quite powerful computer resources, most examples in this article are restricted to two dimensions assuming plane symmetry and can easily be extended for 3D analyses.