# A damage and failure implementation for the simulation of ductile solids with Total-Lagrangian Smooth Particle Hydrodynamics

## TL;DR

This paper introduces a new damage and failure model for Total-Lagrangian SPH to better simulate ductile solids under large deformations, incorporating damage criteria and validated against experiments and FEM results.

## Contribution

It develops a novel damage and failure model for TLSPH that accounts for material property changes and discontinuities, improving ductile solid simulations.

## Key findings

- The new model accurately predicts damage initiation and growth in ductile materials.
- Validation shows improved agreement with experimental data and FEM simulations.
- The implementation enhances TLSPH's stability and predictive capabilities for ductile failure.

## Abstract

Smooth-Particle-Hydrodynamics is gaining popularity for the simulation of solids subjected to machining, wear, and impacts. Its attractiveness is due to its abilities to simulate problems involving large deformations resulting from the absence of mesh, recent improvements in stability conferred by the development of Total-Lagrangian version of SPH (TLSPH), but also its availability in the open-source software LAMMPS. This implementation features a damage model similar to the `pseudo-spring' method which creates instabilities when used for the simulation of ductile materials. In this contribution, we present a new damage and failure model for TLSPH suitable for ductile materials. In this implementation, not only the constitutive equations but also the TLSPH approximation are modified in order to take into account the change in material properties as well as the presence of discontinuities due to the initiation and growth of damage. This new approach is accompanied by the implementation of the Cockroft-Latham, Johnson-Cook, and Gurson-Tvergaard-Needleman damage criteria. The predictive capabilities of the implementation of this new damage model are then tested and compared against both experimental and results of Finite Element simulations.