Finite deformations of metal cylinders subjected to electromagnetic fields and mechanical forces

Abstract

Strong electromagnetic (EM) fields coupled with mechanical loads may have a profound effect on deforming bodies. The continuum description of the plastic deformation of solids under electric fields and mechanical loads essentially involves the coupling of the field equations of continuum mechanics with Maxwell's equations. This analysis considers the effects of large EM fields on solid metal cylinders undergoing plastic deformations. Other researchers have used an electroplastic effect to explain previous EM and mechanically loaded experimental results. We examine whether it is necessary to invoke this controversial mechanism. First, we consider only EM loading and solve the transient EM distribution in a solid metal cylinder. This determines the EM time scales as compared to thermal diffusion time scales. Next, at the continuum level, we present the mechanical problem of quasi-static finite compressive deformations incorporating thermal expansion, strain hardening, strain rate sensitivity, thermal softening, and heat conduction. A viscoplastic model that is applicable over a wide range of strain rates (10 −4–10 6 s −1) characterizes the material response. Finally, we consider a metal cylinder subjected to uni-axial mechanical loading as well as high axial current pulses. The material is assumed to be isotropic with the plastic incompressibility constraint. The deformations are assumed to remain axisymmetric and no instabilities in the cylinder are considered. Coupled effects of Joule heating and the Lorentz force on the quasi-static deformations are examined.