Universal relations for electro-magneto-active solids in shear and triaxial extension

In light of recent and growing interest in soft electro-magneto-active materials, this letter addresses the problem of an isotropic, nonlinear elastic, incompressible electro-magneto-active solid cube undergoing homogeneous deformation due to shear and triaxial extension with no normal tractions applied. This cube generally undergoes dimensional changes due to shear deformation and the Poynting effect with no electromagnetic field. This short article is devoted to analytically examine the impact of electromagnetic fields on these dimensional changes, developing the constitutive equations for nonlinear electro-magneto-active solids. The purely geometric universal relations are established for the cube deformation, directly linking the shear, the electric field, the magnetic field, and the stretch. Such a direct linkage of kinematical quantities-based universal relations provides an essential feature of being easily tested experimentally. Existing universal relations with no electromagnetic field validate the developed relations.