Research On Multi Field Coupling Problem Of Two Two Dimensional Elastic Bodies Based On Fractional Order Thermoelastic Theory

The classical heat conduction theory of Fourier holds that the speed of heat transfer is infinite,but it is only suitable for the state where the heat transfer time is long enough and the heat transfer tends to be stable.But with the emergence of new materials and the study of extreme heat transfer conditions,for unsteady heat transfer processes and extreme heat transfer conditions,such as microscale heat transfer,ultra-low temperature heat transfer,etc.,the results predicted by classical theory are inconsistent with those observed by experiment.Therefore,the thermoelastic coupling theory and the generalized thermoelastic theory are presented,and it is proposed that the wave propagates in the medium at a finite velocity.The widely used generalized thermoelastic coupling theories are: Lord-Shulman(L-S)theory(including one thermal relaxation time),Green-Lindsay(G-L)theory(including two thermal relaxation times)and Green-Naghdi(G-N)theory(no energy dissipation).For some special materials,such as viscoelastic materials,piezoelectric materials,multi-void materials,and some special physical processes,such as abnormal heat transfer,abnormal diffusion,etc.,the classical heat conduction theory and the generalized thermoelastic theory are not enough to describe the thermoelastic behavior.Therefore,on the basis of the generalized thermoelastic theory,the Fractional Calculus is introduced,especially in the fields of microscale effect,heat conduction and so on,to correct the coupling mechanical problems of multi-physical fields such as electromagnetic thermoelasticity.The fractional order differential and integral theory is developed continuously,and the fractional order differential and integral operator is introduced to modify the heat conduction equation.Because the application of Ezzat Fractional order generalized thermoelastic theory is relatively few,in order to study this theory deeply,this paper based on Ezzat Fractional order generalized thermoelastic theory,applies the regular mode method,the coupling problem of multi-physical fields in a semi-infinite thermoelastic model is studied.The main contents are as follows:(1)based on the Ezzat Fractional order generalized thermoelastic theory,the thermoelastic coupling problem of two dimensional fiber reinforced elastomer under the action of linear type I crack is studied,and the corresponding differential equation are obtained,the regular mode method is applied to solve the equations,and the concrete function expressions are obtained,then the exact solutions of each physical quantity are obtained,and the distribution trend images of dimensionless stress,displacement and temperature are drawn.The results show that the changes of fractional order parameter,rotation and crack size have significant effects on the calculated stress,displacement and temperature.(2)Based on the Ezzat fractional generalized thermoelastic theory,the effects of gravity on wave propagation in an infinite piezoelectric medium in half-space under periodic loading are investigated.In this paper,the control equations under fractional order generalized thermoelastic theory are given,and the regular mode method is used to solve the control equations,the distribution of dimensionless temperature,displacement,stress and electric displacement in an infinite piezoelectric medium in half space is obtained.The effects of fractional order parameters and gravity on physical quantities are studied in detail.The results show that the thermoelastic coupling effect appears in the infinite piezoelectric medium in half-space due to the periodic load.