# Multi-physics simulations of lightning strike on elastoplastic substrates

## TL;DR

This paper introduces a novel multiphysics simulation method that models the two-way interaction between lightning plasma arcs and elastoplastic aerospace materials, capturing dynamic feedback and topological evolution.

## Contribution

The work presents the first two-way coupled model solving magnetohydrodynamic and elastoplastic equations simultaneously for lightning-material interactions.

## Key findings

- Accurately reproduces plasma arc growth dependent on substrate conductivity.
- Demonstrates distinct behaviors in multi-layered and temperature-dependent substrates.
- Validates model against experimental laboratory studies.

## Abstract

This work is concerned with the numerical simulation of elastoplastic, electromagnetic and thermal response of aerospace materials due to their interaction with a plasma arc under lightning strike conditions. Current approaches treat the interaction between these two states of matter either in a decoupled manner or through one-way coupled 'co-simulation'. In this paper a methodology for multiphysics simulations of two-way interaction between lightning and elastoplastic materials is presented, which can inherently capture the non-linear feedback between these two states of matter. This is achieved by simultaneously solving the magnetohydrodynamic and the elastoplastic systems of equations on the same computational mesh, evolving the magnetic and electric fields dynamically. The resulting model allows for the topological evolution and movement of the arc attachment point coupled to the structural response and Joule heating of the substrate. The dynamic communication between the elastoplastic material and the plasma is facilitated by means of Riemann problem-based ghost fluid methods. This two-way coupling, to the best of the authors' knowledge, has not been previously demonstrated. The proposed model is first validated against experimental laboratory studies, demonstrating that the growth of the plasma arc can be accurately reproduced, dependent on the electrical conductivity of the substrate. It is then subsequently evaluated in a setting where the dynamically-evolved properties within the substrate feed back into the plasma arc attachment. Results are presented for multi-layered substrates of different materials, and for a substrate with temperature-dependent electrical conductivity. It is demonstrated that these conditions generate distinct behaviour due to the interaction between the plasma arc and the substrate.