# Dynamic fracture of a discrete media under moving load

## TL;DR

This paper investigates how a moving load influences crack propagation in a simple lattice model, analyzing steady-state regimes, energy-speed relations, and the effects of load parameters through analytical and numerical methods.

## Contribution

It introduces a combined analytical and numerical study of crack dynamics under moving loads in a lattice, revealing steady-state regimes and forbidden regimes in fracture processes.

## Key findings

- Existence of steady-state crack speeds related to load parameters
- Identification of forbidden regimes in force and energy perspectives
- Numerical simulations showing various approaches to steady-state

## Abstract

Most of the research concerting crack propagation in discrete media is concerned with specific types of external loading: displacements on the boundaries, or constant energy fluxes or feeding waves originating from infinity. In this paper the action of a moving load is analysed on the simplest lattice model: a thin strip, where the fault propagating in its middle portion as the result of the moving force acting on the destroyed part of the structure. We study both analytically and numerically how the load amplitude and its velocity influence the possible solution, and specifically the way the fracture process reaches its steady-state regime. We present the relation between the possible steady-state crack speed and the loading parameters, as well as the energy release rate. In particular, we show that there exists a class of loading regime corresponding to each point on the energy-speed diagram (and thus determine the same limiting steady-state regime). The phenomenon of the forbidden regimes is discussed in detail, from both the points of view of force and energy. For a sufficiently anisotropic structure, we find a stable steady-state propagation corresponding to the slow crack. Numerical simulations reveal various ways by which the process approaches - or fails to approach - the steady-state regime. The results extend our understanding of fracture processes in discrete structures, and reveal some new questions that should be addressed.