Do we need to recourse to Ampère - Neumann electrodynamics to explain wire fragmentation in the solid state ?

Exploding wires are widely used in many experimental setups and pulsed power systems. However, many aspects of the process of wire fragmentation still remain unclear. If the current density is not too high, the wire may break up in the solid state. The experiments have shown that the wires break in tension due to longitudinal forces of unknown nature. In a series of papers, see [2, 3, 4, 5] Graneau argued that neither mechanical vibrations induced by the electromagnetic pinch force nor thermal expansion could have been responsible for the wire disintegration because they were too weak. To explain the phenomenon he appealed to the obsolete Ampère force law as opposed to the conventional Biot-Savart force law. Graneau argued that the Ampère force law would lead to a longitudinal tension in the wire, although his calculations may have been in error on this point. Therefore, Graneau's explanations induced a controversy in electrodynamics with a number of authors arguing pro and con. Previous theoretical and numerical investigations served to provide a search for these forces without recourse to unconventional electrodynamics have identified the pinch effect and thermal expansion as a source of strong longitudinal vibrations. But the tensile stress component has been proved to be present only in the wires having free ends. Thus the mechanism doesn't give a satisfactory explanation of the phenomenon in the wires with clumped ends. In this investigation, we use a simplified magneto-thermo-elastic model to study flexural vibrations induced by high pulsed currents in wires with clumped ends on account of their role in the disintegration process. Several aspects are studied, namely (i) the buckling instability due to simultaneous action of the thermal expansion and the magnetic force, (ii) the flexural vibrations induced in initially bent wires. It is shown that the induced flexural vibrations are strong enough to lead to the breaking of the wire in a wide range of parameters.