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Laboratory for Scientific Computing


Lightning strike on aircraft can lead to serious damage, especially to composite materials, which have low thermal and electrical conductivity. Thorough testing of materials used for aircraft is therefore essential to ensure they can withstand a strike in flight. Numerical simulations can dramatically reduce the time and cost of experimental tests, but this is beyond the capability of current commercial software. To this end, we have developed and applied a multi-physics model of plasma-elastoplastic material interaction.


This project is funded by Boeing Reaserch & Technology. 

The challenge

By coupling the resistive magnetohydrodynamics equations for a plasma and the elastic-plastic equations for a solid, we can capture the non-linear effects and feedback of a lightning strike against a range of material substrates.

The simulation of lightning requires coupling of the Euler equations for fluid dynamics and Maxwell’s equations for magnetic fields.  This system must then also be coupled to the elastic-plastic substrate, such that current flow and energy deposition (Joule heating) effects within the substrate may be captured.  The high temperatures during the process necessitate the solution of complex equation of state for the plasma arc.

The research

Small scale experiments aim to replicate and understand the effects of lightning damage to an aircraft panel. The objective of this work is to simulate these experiments and provide information which cannot be recovered by direct measurement.  The plasma is modelled through a 19-species equation of state, which can capture the ionisation of the key species in air in a continuum model.

Current flow and magnetic field are computed dynamically, and are dependent on the electrical conductivity within the plasma arc (the strike) and the properties of the substrate.  Typically we consider a current flow from an electrode, through the plasma arc and into a substrate, which is grounded.

The coupled plasma/substrate model is a complex multiphysics problem and the interaction between the plasma and elastic-plastic components (which could be one or more substrates, and the electrode) is facilitated through a sharp interface ghost fluid method.  The hyperbolic equations of motion are coupled with elliptic methods to solve for current density and magnetic field.


Experimental studies show that the electrical conductivity of a substrate can have a substantial effect on the structure of plasma arc attachment.  We can use this as validation for our model by simulating arc attachment to two different materials, aluminium and an isotropic composite-like material.  For an aluminium plate, the electrical conductivity of the substrate is far greater than that of the plasma, and the plasma arc takes the most direct path to the substrate.  For composite materials, the electrical conductivity of the arc and the substrate are comparable, and thus the plasma arc tends towards taking the shortest route to the ground site.  The temperature profile for the two substrate materials are shown, with the wide arc attachment site clearly visible for the composite-like substrate.  The low conductivity of the substrate is also apparent in the large temperature rise within the substrate itself.

Typically, an aircraft fuselage is not made of a single material, but a layered composition.  In this case, it is not necessarily the outer material that governs the behaviour of a lightning strike.  We demonstrate this effect by placing a layer of aluminium beneath a layer of composite-like material.  When comparing this to impact against only a single layer of composite-like substrate, we see that despite impacting the same material first, the behaviour of the plasma arc is very different.  This is due to the current taking a preferential path through the aluminium substrate, rather than through the  top composite-like layer, as shown by the current density streamlines in the figure below.


  • A numerical methodology for simulating plasma arc-induced detonations, Michael L., Millmore S.T., and Nikiforakis N., 16th International Detonation Symposium Proceedings (2018)
  • A multiphysics formulation for modelling lightning strike on elastic-plastic substrates, S. Millmore and  N. Nikiforakis  2109 (in preparation).
  • An Equation of State for air plasma modelling, F. Träuble, S. Millmore and N. Nikiforakis, 2019 (in preparation)
  • Comparison of grey body, NEC, P 1 and SP-3 models for numerical simulation of lightning strikes, M. Apsley, S. Millmore and N. Nikiforakis 2019 (in preparation)
  • Numerical simulation of lightning strike on coated elastic-plastic substrates, W. P. Bennett, S. Millmore and N. Nikiforakis 2019 (in preparation)

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