Study On Generalized Thermoelastic Problem Considering Strain Rate

Classical heat transfer theory shows that no matter what happens to the heat transfer mechanism,it should obey Fourier's law and propagate at infinite speed.For conventional steady-state heat conduction,Fourier's law is accurate enough to describe the relationship between heat flux and temperature gradients.However,in some transient cases,its applicability is doubtful.In order to overcome the paradox of heat propagation in the medium at infinite speed based on the classical heat conduction theory and to describe the fluctuation of heat conduction,scholars have established the non-Fourier heat conduction law.In fact,heat conduction will inevitably cause temperature changes and generate thermal stresses in the structure.Therefore,it is particularly important to analyze the thermoelastic coupling response of the structure in the thermal environment,which is an indispensable method for predicting whether the structure can operate safely.Scholars have proposed several theories describing transient thermoelastic response,which are often called generalized thermoelastic theory.Using these theories,one can consider the transient response of structures in extreme temperature environments.Lord and Shulman established the L-S generalized thermoelastic theory.Green and Lindsay established the G-L generalized thermoelastic theory.Green and Naghdi proposed a generalized thermo-elastic theory of G–N that does not consume energy based on the entropy balance equation and energy balance.The above three theories can describe the thermal wave effect and the coupling effect between the temperature field and the deformation field.To describe the thermoelastic behavior of piezoelectric materials,Mindlin established a classic thermopiezoelectric theory and studied the thermoelastic behavior of thermopiezoelectric plates.Based on the laws of thermodynamics and GL thermoelasticity theory,Chandrasekharaiah extended Mindlin theory and established a generalized Linear theory of piezoelectric thermoelastic coupling.So far,considering the strain relaxation phenomenon of the material itself,that is,the generalized thermoelastic theory considering the strain rate is relatively few.In order to more truly reflect the deformation mechanism of the material,this paper introduces the strain rate on the basis of the existing theory,and studies the following content:(1)By introducing strain rate,based on Chandrasekharaiah's generalized piezoelectric thermoelastic theory,after expansion,a generalized piezoelectric thermoelastic theory considering strain rate was established.With the help of the laws of thermodynamics,the establishment process of the theory is given and the corresponding state equations and control equations are obtained.In the constitutive equation,the product term of the strain relaxationtime and the strain rate is introduced.At the same time,the thermal relaxation time factor is introduced in the constitutive equation and the energy equation,respectively.Later,the theory was used to study the dynamic response of the one-dimensional piezoelectric thermoelastic problem under the action of 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 times,that is,the distribution law of dimensionless temperature,displacement,stress and electric potential is obtained,and it is represented graphically..The results show that the strain rate has a significant effect on the distribution of temperature,displacement,stress and electric potential.(2)In the context of generalized thermoelastic theory considering strain rate,the transient response of a half-space heated by a non-Gaussian laser beam on the boundary is studied.The calculation results show that with the decrease of the strain hysteresis factor,the absolute value of the dimensionless temperature peak,the displacement and the stress peak increase;when the functional gradient parameter is less than zero,the negative temperature value,the positive displacement and the stress value will appear.