Principle of virtual power applied to deformable semiconductors with strain, polarization, and magnetization gradients

The aim of this article is to generalize previous works in order to provide a systematic method to derive the equilibrium equations and the constitutive ones for deformable semiconductors accounting for first-order strain, polarization, and magnetization gradients. This is done by use of the ``principle of virtual power'' subject to the objectivity requirement (i.e., translational and rotational invariances) to which we add the first and the second laws of thermodynamics associated with the conservation of energy and the entropy production. This leads to a generalized expression of the Clausius-Duhem inequality, from which constitutive equations are derived. The interactions of the electromagnetic fields with the deformable and the semiconducting continua appear naturally by generalized non-symmetric stress tensors and the body and surface forces of electromagnetic origin. A comparison with some previous works is made putting emphasis on flexoelectricity that will be dealt with in a future work. Finally, special attention is given to particular cases relative to dissipative phenomena associated with semiconducting properties. In order to be close to what is nowadays done by physicists, the SI units have replaced the Lorentz-Heaviside units often used in previous works.