# Numerical Modelling of Crack Initiation, Propagation and Branching under Dynamic Loading

## TL;DR

This paper presents a novel pseudo-spring SPH method to simulate crack initiation, propagation, and branching under dynamic loading in 2D and 3D, showing good agreement with experimental results.

## Contribution

The paper introduces a pseudo-spring analogy in SPH for damage modeling, enabling accurate simulation of complex crack behaviors in dynamic conditions.

## Key findings

- Crack speeds and paths match experimental data
- Crack branching and surface evolution are effectively modeled
- Framework successfully simulates 3D crack phenomena

## Abstract

In this paper crack initiation, propagation and branching phenomena are simulated using the Pseudo-Spring Smooth Particle Hydrodynamics (SPH) in two and three-dimensional domains. The pseudo-spring analogy is used to model material damage. Here, the interaction of particles is limited to its initial immediate neighbours. The particles are connected via springs. These springs do not provide any extra stiffness in the system but only define the level of interaction between the connecting pairs. It is assumed that a crack has passed through a spring connecting a particle pair if the damage indicator of that spring becomes more than a predefined value. The crack branching of a pre-notched plate under dynamic loading and the effect of loading amplitude are studied here. The computed crack speeds, crack paths and surfaces are compared with experimental and numerical results available in the literature and are found to be in good agreement. The effect of notch location for a plate with a circular hole is studied here. The ability of the framework to model arbitrary crack paths and surfaces are demonstrated via three-dimensional simulations of chalk under torsion, Kalthoff-Winkler experiment and Taylor bullet impact.