A note on the inhomogeneous shear for a class of visco-electro-elastic slab. A parametric study

A boundary value problem is studied for a class of electro-visco-elastic semi-infinite slab, considering constitutive equations, wherein the deviatoric part of the symmetric stress tensor, and the electric displacement, are assumed to be functions of the left Cauchy–Green tensor, the symmetric part of the velocity gradient, and the electric field. The boundary value problem being studied corresponds to a class of inhomogeneous shear for a slab, under the influence of an electric field acting transversely to that body. Two (in general nonlinear) equations are obtained, which can be used to determine the shear deformation and the electric field inside the slab. Considering some further simplifications such equations are reduced to one linear partial differential equation for the shear deformation. The main equation and the different variables are put into dimensionless forms, and the dimensionless equivalent partial differential equation is solved exactly for some particular boundary and initial conditions. Such solutions are still valid for the case of large deformations. Some numerical results are presented, evaluating the exact solution for different values for some of the material parameters of the problem (in dimensionless forms). The main idea is to study the effect of electric fields in the behaviour of the slab.