Modelling of instabilities in magnetoelastic membranes Thin materials may exhibit instabilities when placed under large loads. In addition to the commonly known buckling phenomena that occurs under compressive loading, thin tubular membranes also demonstrate a further limit point elastic instability leading to sudden large deformations when placed under hydrostatic load. Magnetoelastic membranes, that may have application in structural and aerospace engineering for example, are subject to further limit point instabilities related to an applied magnetic load. It is desired that the unstable beha- viour of these magnetic field-responsive tubular membranes be examined using computational methods. This work would entail • the implementation and validation of a 2-d axisymmetric formulation for the quasi- static magento-elastic problem using the scalar potential formulation. This will be used to model the magnetoelastic material and surrounding free-space through which the magnetic field permeates; • the implementation of an adaptive meshing scheme to accurately capture the response of the thin structure; and • the implementation of a robust non-linear scheme from the literature to render the solution under unstable conditions.
This work will be conducted using the open-source, high-performance deal.II finite element library.