Total Lagrangian Smoothed Particle Hydrodynamics with An Improved Bond-Based Deformation Gradient for Large Strain Solid Dynamics

TL;DR

This paper introduces an improved bond-based deformation gradient calculation in Total Lagrangian SPH to enhance accuracy and stability in large strain solid dynamics simulations, reducing zero-energy mode issues.

Contribution

It proposes a novel bond-based deformation gradient method with kernel correction, improving stability and accuracy in large strain solid simulations within TLSPH.

Findings

Enhanced stability in large strain simulations

Improved convergence demonstrated in benchmarks

Robustness confirmed in 3D examples

Abstract

Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) is one variant of SPH where the variables are described using the fixed reference configuration and a Lagrangian smoothing kernel. TLSPH elevates the computational efficiency of the standard SPH when no topological change is involved, and it alleviates the stability of SPH scheme with respect to tensile loading. However, instabilities associated with spurious mode, or hourglass/zero-energy mode, persists and often affects the simulation of solids undergoing extremely large strain. This work proposes an alternative formulation to compute deformation gradient with improved accuracy and therefore minimising the possibility of encountering the zero-energy mode. Specifically, we leverage the local discrete computation of bond-based (or pairwise) deformation gradient smoothed by the kernel. Additionally, the bond of a particle with itself is considered to preserve the polynomial reproducibility imposed by the kernel correction scheme. We showcase the convergence of the approach using a two-dimensional benchmark example. Furthermore, the accuracy, robustness, and stability of the proposed approach are assessed in various two- and three-dimensional examples, highlighting on the stability improvement that allows for solid dynamic simulations with more extreme elongation.