A new nonlinear magnetoelastic constitutive theory with application to deformation of circular cylindrical tubes

Abstract

Magnetoelasticity theories describe the behavior of solids in response to the application of a magnetic field. This paper presents a new thermodynamically consistent constitutive theory for simulating nonlinear responses of solids for which the strain energy density depends on the deformation gradient through the Biot strain tensor and specializes the theory for application to the problem of finite deformation of a circular cylindrical tube. The derived theory appears to be attractive for applications as it provides a relatively simple mathematical expression for modeling nonlinear magneto-mechanical responses of solids. For the considered problem, it is obtained that a higher modified pressure is required to maintain a specified azimuthal stretch when a magnetic field is applied. Finally, and among other things, it is observed that the influence of the magnetic field can either decline or progressively enhance with increasing azimuthal stretch.