An Electromechanical Micropolar Peridynamic Model for Isotropic and Orthotropic Materials

A micropolar peridynamic model for in-plane electro-mechanical behavior of isotropic and orthotropic solids is presented. The analytical implicit formulation of the electrical part of the model is based on the definition of a proper microelectrical energy function and a specific electrical inelastic deformation parameter. A compatibility condition and a constitutive relationship has been derived and thus the electrical stiffness operator has been obtained. The electrical formulation is then coupled with a mechanical micropolar peridynamic formulation that accounts for full orthotropy and isotropy as special case. A distinctive aspect of the formulation is the use of continuous trigonometric functions, for the mechanical and electrical bond properties with respect to the principal material axes. The obtained unified model is capable to predict the mechanical response and the electrical conduction of elastic brittle materials taking into account the influence of cracks and other defects along with mechanical and/or electrical orthotropy. The proposed model has been applied to predict the electric field potential in isotropic and orthotropic square laminae, and to simulate a coupled electromechanical problem.