A generalized piezoelectric-thermoelastic theory with strain rate and its application

The deformation of a large number of materials in engineering is between elasticity and viscosity, which exhibits both features of elastic solid and viscous fluid, that is, viscoelasticity. Viscoelasticity causes many mechanical relaxation phenomena, such as strain relaxation and hysteresis loss. In the investigation of transient response of multi-field problems subjected to thermal loading, it is especially important to take the phenomena such as thermal relaxation and the strain relaxation into consideration to accurately describe their transient response. For the transient response of the generalized piezoelectric-thermoelastic problems, although the generalized piezoelectric-thermoelastic model was established by taking into account the thermal relaxation, no strain relaxation is included so far. In present paper, by considering the strain relaxation in the process of deformation, a generalized piezoelectric-thermoelastic theory is theoretically established by extending Chandrasekharaiah's theory through taking strain rate into consideration. By means of the thermodynamic laws, the theory is formulated and the corresponding state equations and governing equations are obtained. In constitutive equation, a term of the product of a strain relaxation time and the strain rate is introduced, meanwhile, thermal relaxation time factors are included in constitutive equation and energy equation respectively. Subsequently, this theory is applied to investigating the dynamic response of a one-dimensional piezoelectric-thermoelastic problem subjected to a moving heat source. The Laplace transform and its numerical inverse transform are used to solve the problem, and the transient response under different strain relaxation time and heat source moving speed is obtained, that is, the distribution law of dimensionless temperature, displacement, stress and electric potential. The effect of strain rate on each physical quantity was investigated, and the results were presented in graphical form. The results show that the strain rate has a significant effect on the distributions of temperature, displacement, stress and electric potential. © 2020, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.