Formulation and numerical analysis of a fully-coupled dynamically deforming electromagnetic wire

An electromagnetic beam model is developed for the simulation of actuated electronic textiles. The beam is solved using a nonlinear director-based kinematic description with additional temperature and electric potential fields along its length. The three fields are fully coupled by mutual dependences on the deformation, Lorenz force, back electromotive force, temperature dependent constitutive responses, and the Seebeck effect. Instead of solving Maxwell's equations in full detail, a quasistatic approximation is used to solve the electric potential in the presence of a moving material medium. The current-carrying beam approximation is used to further simplify the solution space for the potential. While this formulation alleviates the spatial and temporal discretization restrictions, the coupled problem is an index-1 semi-explicit Differential Algebraic Equation requiring special treatment. The time dependent problem is solved using different Runge-Kutta methods. Diagonally implicit Runge-Kutta methods and explicit Runge-Kutta methods using implicit solution of the electric potential problem are explored. The finite element model is implemented using the open source package FEniCS, which is able to automatically generate the linearizations of the multiphysics equations required for the implicit solutions. A model problem is constructed with which to test and analyze the physical formulation and numerical solution techniques. The time stepping methods are verified using the convergence orders of the higher-order Runge-Kutta methods. Runtime comparisons show that the explicit methods are generally more computationally efficient than the implicit schemes used for this problem. For the implicit schemes, a staggered solution is significantly faster than a monolithic solution at most time step sizes. However, at very large time steps, such as those that would be used for dynamic relaxation, the monolithic solution can be more efficient than the staggered solution.