Material-dependent relations for magneto-active solids undergoing shear and triaxial extension

This article addresses the problem of an isotropic, nonlinear elastic, incompressible magneto-active solid cube undergoing homogeneous deformation due to shear and triaxial extension, with no normal tractions applied. The novel material-dependent relations are established for this deformation, valid for all incompressible magneto-active solids. The considered cube generally undergoes dimensional changes due to shear deformation and the Poynting effect with no magnetic fields. The purpose of this study is to examine the impact of magnetic fields on these dimensional changes, developing the constitutive equations for nonlinear magneto-active solids. Expressions for the dimensional changes are derived as functions of shear and triaxial extension, accounting for different orientations of the magnetic field vectors relative to the shearing direction. Existing universal relations with no magnetic field validate the developed relations.