Generalized smoothed particle hydrodynamics with overset methods in total Lagrangian formulations

TL;DR

This paper introduces a generalized smoothed particle hydrodynamics method with overset techniques in a Total Lagrangian framework, enabling adaptive resolution and improved handling of large deformations and crack propagation.

Contribution

It presents a novel GSPH approach that uses multiple local coordinate spaces to adaptively vary spatial resolution and avoid singularities in complex deformation problems.

Findings

Enables adaptive spatial resolution based on deformation characteristics

Reduces computational cost with fewer particles in complex structures

Successfully applied to large deformation and crack propagation scenarios

Abstract

This study proposes a generalized coordinates based smoothed particle hydrodynamics (GSPH) method with overset methods using a Total Lagrangian (TL) formulation for large deformation and crack propagation problems. In the proposed GSPH, the physical space is decomposed into multiple domains, each of which is mapped to a local coordinate space (generalized space) to avoid coordinate singularities as well as to flexibly change the spatial resolution. The smoothed particle hydrodynamics (SPH) particles are then non-uniformly, e.g., typically in the boundary-conforming way, distributed in the physical space while they are defined uniformly in each generalized space similarly to the normal SPH method, which are numerically related by a coordinate transformation matrix. By solving a governing equation in each generalized space, the shape and size of the SPH kernel can be spatially changed in the physical space so that a spatial resolution is adaptively varied a priori depending on the deformation characteristics, and thus, a low-cost calculation with the less number of particles is achieved in complex shape structures.