3D Beam-to-beam Contact Within Coupled Electromechanical Fields: a Finite Element Model

In this paper a 3D beam-to-beam contact element is presented, to deal with contact problems in the coupled electric - mechanical fields. The beams are supposed to get in contact in a pointwise manner, the detection of the contact points and the computation of all contributions are carried out using a fully symmetric treatment of the two beams. Concerning the mechanical field, Hertz theory of contact for elastic bodies is considered. The contact area is varying according to the beam-to-beam angle, being circular only in the case of perpendicular beams. This variation of the shape is taken into account too. The problem is semi-coupled: the me-chanical field influences the electric one because of the dependence of the voltage distribution on the contact area. Within the finite element discretization, the mechanical and the electric treatment of the beam element is formulated in the usual way, considering nodal displacements and voltages as main unknowns. The electromechani-cal contact constraints are enforced with the penalty method. Starting from the virtual work equation the consistent linearization of all contributions is computed to achieve the quadratic convergence within the Newton-Raphson iterative scheme. The complete set of equations - arranged in a matrix form suitable for the finite element implementation - is solved with a monolithic approach. Finally some numerical examples are discussed to show the effectiveness of the model.