# Numerical Simulation of Metal Machining Process with Eulerian and Total Lagrangian SPH

## TL;DR

This study compares Eulerian and Total Lagrangian SPH methods for simulating metal machining, demonstrating that TLSPH offers improved stability and accuracy in modeling strain localization and chip formation.

## Contribution

The paper introduces the application of TLSPH to metal machining, highlighting its advantages over ESPH in stability and simulation fidelity.

## Key findings

- Both SPH methods capture key metal processing phenomena.
- TLSPH provides better strain localization and chip morphology.
- TLSPH is more stable and efficient for machining simulations.

## Abstract

This paper presents numerical simulations of metal machining processes with Eulerian and Total Lagrangian Smoothed Particle Hydrodynamics (SPH). Being a mesh-free method, SPH can conveniently handle large deformation and material separation. However, the Eulerian SPH (ESPH) in which the kernel functions are computed based on the current particle positions suffers from the tensile instability. The Total Lagrangian SPH (TLSPH) is free of this instability as the kernel functions are calculated in the reference configurations. In this work, the metals are modelled using the Johnson-Cook constitutive model, which can capture strain hardening and thermal softening in metals. The processing/cutting tools are modelled as rigid bodies, while the metal-tool contact forces are considered using the standard SPH interaction and the particle-particle pinball contact in ESPH and TLSPH, respectively. The two methods are employed to model several cases with impact, pressing, and cutting; the results are compared with reference experimental and numerical results. It is found that both the two SPH methods can capture the salient phenomena in metal processing, e.g. strain localisation, large deformation, and material separation. However, the TLSPH approach provides a better simulation of strain localisation and chip morphology. This work shows that the TLSPH method has the potential to model the metal machining processes efficiently without any numerical instabilities.