Finite element modeling of thermopiezomagnetic smart structures

Linear constitutive equations of a thermopiezomagnetic medium involving mechanical, electrical, magnetic, and thermal fields are presented with the aid of a thermodynamic potential. A thermopiezomagnetic medium can be formed by bonding together a piezoelectric and magnetostrictive composite. Two energy functionals are defined. It is shown via Hamilton's principle that these functionals yield the equations of motion for the mechanical field, Maxwell's equilibrium equations for the electrical and magnetic fields, and the generalized heat equation for the thermal field. Finite element equations for the thermopiezomagnetic media are obtained by using the linear constitutive equations in Hamilton's principle together with the finite element approximations. The finite element equations are utilized on an example two-layer smart structure, which consists of a piezoceramic (barium titanate) layer at the bottom and a magnetoceramic (cobalt ferrite) layer at the top. An electrostatic field applied to the piezoceramic layer causes strain in the structure. This strain then produces magnetic field in the magnetoceramic layer.