Multiple Spatial And Temporal Scales Method For Thermal Shock Problems Of Periodic Multiphase Materials

Thermal shock is an important problem which is especially considered in material designand study. As an experimental law, Fourier Law describes the heat diffusion phenomena withthe assumption that the heat propagation speed of the thermal disturbance is infinite. It isaccurate enough for most practical problems, such as the steady heat conduction and heatpropagation in longer work time or with lower load strength and the non-steady heatconduction with more rapid heat propagation speed. However, to thermal shock problems, thefinite heat propagation speed must be taken into account for the non-steady heat conductionunder the extremely conditions such as heat conduction problems at micro-spatial andtemporal scales. At this time, there will be different from the general heat transfer process ofphysical phenomena, which has been known as non-Fourier effect of heat conduction.In recent years, along with the widely use of high-performance composite materials insome application such as Micro Electronical Mechanical Systems and Thermal BarrierCoating System etc., micro-scale heat conduction has become hotspot of research andapplication. To the analysis of mechanical property of materials, the finite element methodbased on the classical continuum theory has been used in a wide range of engineering areasdue to the high effect and flexibility. But to the composite materials with microstructure, themultiple scale problems will lead to spend vast computing power because of the strongheterogeneity of these materials. To solve the difficulty of the computation associated withvarious scales in practical engineering, the multiple scales methods have been used and arewidely concerned.In this thesis, non-Fourier heat conduction problem in periodic materials withmicrostructure is systematically studied by a multiple spatial and temporal scales method. Anamplified spatial scale and a reduced temporal scale are introduced, and the high-ordernon-local differential equation of heat conduction with fourth-order spatial derivative isderived by combining the different orders of the homogenized non-Fourier heat conductionequations and eliminating the reduced temporal scale. To avoid the necessity of C~1-continuityin finite element implementation, the new high-order nonlocal equation with C~0-continuity,which contains a mixed second-order derivative in space and time, is put forward to study thefluctuation and the dispersion effect of non-Fourier heat conduction due to spatialheterogeneity. Based on finite element discrete scheme, two dimensional numerical examplesunder various work conditions are computed, and the results show the validity and efficiency of the developed high-order nonlocal model, which is compared with the fine finite elementmodel and the classical homogenization model.