Finite element models for use in mechanics including geological engineering

A number of finite element (FE) models have been developed, starting with a purely magnetic one. The magnetic model was verified against analytical solutions and the commercial FE-programme ANSYS. The magnetic model was then coupled to the wave-equation, resulting in a model governing linear magnetostriction. In the magnetostrictive model a property of two degrees of freedom, that is, displacements, was coupled to a property of one degree of freedom, that is, magnetic potential. To make this possible, non-quadratic coupling matrices had to be developed. This linear model was then verified against analytical solutions, with a good conceptual agreement. In the next step the still linear system of equations was time-propagated, using the Newmark method. This model was verified by comparing the differential step-response of the system calculated with the time propagation method, to the frequency function of the system, calculated with the harmonic model. Further, non-linear and non-linear transient models were developed and discussed. The non-linear transient model was developed for a situation where a Terfenol rod was assumed to collide periodically with a rigid wall, thus indicating a tool for analysing a Terfenol based resonant system, which could be used, for example, for ultrasonic cutting of hard and brittle materials and also for rock-blasting.