Investigations On Two-dimensional Multi-field Coupling Problem Under Fractional Order Thermoelastic Theory

The classical Fourier heat transfer theory holds that the velocity of heat propagation in the medium is infinite and the heat flow is proportional to the temperature.If the heat transfer time is long enough and the heat transfer state tends to be stable,the results are accurate by applying the classical heat transfer theory.If the heat transfer process is an unsteady state process and the heat transfer conditions are extreme,such as ultra-high temperature heat transfer,ultra-low temperature heat transfer and micro-scale heat transfer,the classical Fourier heat transfer theory is no longer applicable,that is,the so-called non-Fourier heat transfer phenomenon occurs.With the development of non-fourier heat transfer theory,thermo-elastic coupling theory also appeared,and pointed out the existence of heat wave with finite velocity propagation,and then the generalized thermo elastic coupling theory was put forward.The present generalized thermoelastic coupling theory mainly includes Lord-Shulman(L-S)theory with one thermal relaxation time,Green-Lindsay(G-L)theory with two thermal relaxation times,and Green-Naghdi(G-N)theory with no energy dissipation.For some special materials,such as multi-hole materials,viscoelastic materials,etc.,and some physical processes,such as anomalous diffusion,abnormal conduction,etc.,their thermoelastic behavior has been unable to be accurately described by classical thermoelastic theory and generalized thermoelastic theory.After fractional calculus was used to solve integral equations in equal time problems,fractional calculus has been widely used in various fields,and has corrected many existing physical models of electromagnetic thermoelastic multi-field coupling,especially in the fields of material diffusion,heat conduction and solid mechanics,etc.Therefore,fractional order calculus operators are gradually introduced into the heat conduction equation,and the fractional order calculus theory is further developed,with which the fractional order generalized thermoelastic coupling theory is established.Nowadays,two fractional order generalized thermoelastic coupling theories,Sherief type and Youssef type,are widely used.With Sherief type fractional order generalized thermoelastic coupling theory,two dimensional multifield coupling problem are studied by using the normal mode method.The specific content is as follows:(1)With the fractional order generalized thermoelastic coupling theory proposed by Sherief et al.,we studied the fibre-reinforced two-dimensional problem of thermoelasticity for an infinite space weakened by a finite linear opening mode-I crack.The normal mode method is applied to obtaining the distributions of the non-dimensional temperature,displacement and stress.The results show that fractional order parameters,rotation and crack size have significant effects on the considered variables.(2)With the fractional order generalized thermoelastic coupling theory proposed by Sherief et al.,the two-dimensional electromagnetic thermoelastic problem of infinite semi-space elastomers subjected to thermal shock loading is studied.The dynamic responses of the non-dimensional temperature,displacement and stress are obtained by using the normal mode method.The results show that the magnitude of fractional parameters and the presence or absence of magnetic field have significant influence on the considered variables.