On constitutive equations for anisotropic nonlinearly piezoelectric materials (Q634479)

Summary: The elastic-piezoelectric continuum is investigated theoretically and its non-linear constitutive equations are defined. The theory is formulated in the context of continuum electrodynamics. The solid medium is assumed to be nonlinear, homogeneous, compressible and isothermal, and to have elastic and piezoelectric anisotropy. Basic principles of modern continuum mechanics and balance equations of electrostatics have provided guidance and are determining in the process of this study. From the formulation belonging to the constitutive equations, it is observed that the symmetric stress and polarization are derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it is determined that the free energy function is dependent on a symmetric tensor and a vector. The free energy function is represented by a power series expansion, and the type and number of terms taken into consideration in this series expansion determine the nonlinearity of the medium. Finally, the quasi-linear constitutive equations are substituted in the balance equations to obtain the field equations.