Research On Two-temperature Generalized Magnetothermal-elastic Coupling Problem Based On Non-local And Memory Effects

In the classical heat conduction theory,people think that heat travels at infinite speed.Fourier heat conduction theory is accurate enough for transient or steady heat conduction process under space macro and long-time action.This statement is not consistent with the actual experimental results.With the progress of science and technology and the improvement of the accuracy requirements in engineering practice,this theory can no longer meet the needs,and then the non-Fourier heat conduction theory has been derived.Scholars call this theory and the associated thermoelastic theory as the generalized thermoelastic theory.It mainly includes: introducing a Lord-Shulman(L-S)theory of thermal relaxation time into the heat conduction equation;The thermal relaxation factor is introduced into the constitutive equation and the energy equation respectively,and the Green-Lindsay(G-L)theory of temperature change rate is introduced into the heat conduction equation;And Green-Naghdi(G-N)theory without considering energy dissipation.With the wide application of fractional calculus,scholars have introduced it into the heat conduction equation,further improving the generalized thermoelastic theory,and more accurately describing the thermoelastic behavior of m aterials under extreme heat and mass transfer conditions.Inspired by the fractional-order generalized thermoelastic theory,scholars introduced the modified fractional-order differential(memory-dependent differential)into the heat conduction equation,a nd established the memory-dependent generalized thermoelastic theory,which can more accurately and objectively describe the memory dependence and global correlation of materials,further improving the shortcomings of the fractional-order generalized thermoelastic theory.With the development of smart materials such as piezoelectric materials,the electromagnetic thermoelastic coupling problem based on the generalized thermoelastic theory has been paid more attention by more scholars,and has been studied b y different methods.The main research contents and work of this paper are as follows:(1)Based on the two-temperature generalized magnetothermoelasticity theory of non-local and memory-dependent differentiation,a two-dimensional isotropic uniform elastomer model is established.The thermal shock effect(no stress on the external surface)of the model under constant magnetic field changes with time is studied,and the dynamic response of the non-local effect and memory-dependent effect is considered.The governing equation of this problem is established and solved by integral transformation and numerical inverse transformation.The distribution of time,non-local parameters,time delay factor,dimensionless displacement,temperature and stress under the linear kernel function and the influence of time delay factor under the nonlinear kernel function on each physical quantity are studied successively.(2)Based on Sherief’s fractional order two-temperature generalized magnetothermoelasticity theory,a two-dimensional isotropic uniform elastomer model is established to study the time-varying thermal shock(no stress on the external surface)in a constant magnetic field,and the dynamic response caused by non-local parameters and fractional order parameters is considered.The governing equation of this problem is established and solved by integral transformation and numerical inverse transformation.The dimensionless,temperature and stress distributions of time,non-local,fractional order parameters and double temperature parameters under linear kernel function are studied successively.(3)Based on fractional order Ezzat type Two-temperature generalized magnetothermoelastic theory,two-dimensional isotropic homogeneous elastic body model is set up,research in constant magnetic field at the same time,considering the local effect and fractional order effect and initial static stress caused by the magnetic-hot-water dynamic response problems.The governing equation of this problem is established and solved by regular mode method.The distribution laws of dimensionless displacement,temperature and stress with fractional order parameters,two-temperature parameters,hydrostatic pressure and non-local parameters are studied successively.