Generalized piezoelectric thermoelasticity problems with strain rate and transient thermo-electromechanical responses analysis

Piezoelectric materials have become one of the most promising candidates for a new class of smart structures which are widely used as sensors and actuators in control systems due to their superior electromechanical performance and high-efficiency in electro-mechanical energy conversion. In recent years, although there are many papers of theoretical modeling of generalized piezoelectric thermoelasticity that considered the piezoelectric-thermoelastic coupling of piezoelectric structures serving in the extreme fast heating environment (e.g. ultra-fast laser), the strain relaxation effect has not been considered yet. This work aims to investigate the generalized piezoelectricity problem with strain rate with the aid of extended thermodynamic principles, and corresponding generalized variational theorem is also strictly formulated to provide a complete rationale for numerical method by using semi-inverse method. For numerical evaluation, transient thermo-electromechanical responses of a one-dimensional semi-infinite piezoelectric medium with one end subjecting to a sudden thermal loading are considered and solved by applying Laplace transformation methods. Then the transient responses of temperature, displacement, strain, stress and electric potential are obtained and illustrated graphically, and the influences of strain relaxation parameters on them are also analyzed and discussed.