Numerical solution of some boundary value problems in nonlinear magneto-elasticity

In the context of the theory of nonlinear magneto-elastic deformations, the problem of the extension (shortening) of a cylinder of finite length under the influence of a magnetic field applied far away in free space is studied. The boundary value problem is solved using the finite element method. There exist exact solutions for the problem, which are based on the assumption of working with infinitely long cylinders. In this communication, results are obtained for different relations between the radius of the cylinder and its length, comparing the results for the magnetic field between short and long cylinders. As well as this, the influence of applying such external traction through the direct contact with an external machine has been studied.