Thermodynamic Analysis Of Periodic Multiphase Materials By Spatial And Temporal Multiscale Method

Currently, multiphase materials with periodic microstructures have been widely used inmany advanced engineering applications such as aerospace, aircraft, biomedical, electronicequipment, superconducting coil and so forth. However, the design and use of materials withmicrostructures necessarily involve the related information including both microscopic andmacroscopic scales. This is a major challenge for the materials design. Multiscale modelingtechniques offer an efficient approach for understanding of how different microstructuralproperties affect the average and local response of multiphase materials. Therefore, it isbeneficial to the materials design.Moreover, it is very important subject to study dispersion and attenuation phenomena ofwave propagation in periodic multiphase materials due to successive reflection and refractionwaves from the material interfaces, which may obviously have multiscale characteristics inboth time and space. Possible applications of this research include many domains such asmicrowaves and laser with very high frequency and extremely short duration etc.. However,seldom multiscale methods can be found for studying this problem, so it is believed that wavepropagation in multiphase materials with periodic microstructures deserves furtherinvestigations.The primary research work in this thesis is to study non-Fourier heat conduction andthermal dynamic response in multiphase materials with periodic microstructures underextreme heat impulse and dynamic impact load, which use a spatial and temporal multiscalehigh-order asymptotic homogenization method. To further illustration, one-dimensional caseis studied in this thesis firstly, and the work is extended to multi-dimensional cases. Specificdetails are as follows:A general field equation of thermo-dynamic wave propagation is developed to describeboth the heat transfer and the mechanical behaviour in the periodic multiphase materials undervarious temperature shock and impact load. Amplified spatial and reduced temporal scales are,respectively, introduced by a spatial-temporal multiscale high-order asymptotichomogenization method, and a multiple scale asymptotic expansion is employed toapproximate the transient function field. Different orders of function field equation includingvarious spatial and temporal multiscales are derived. By combining different orders ofhomogenized equations, the high-order nonlocal function field equation with the fourth-orderspatial derivative term is obtained. To avoid the requirement of C~1-continuous finite element formulation and boundary conditions in numerical implementation, the fourth-order spatialderivative term can be approximated by a mixed second-order derivative in space and time.So the C~0-continuous and few boundary conditions are used only. Finally, an approximatedhigher-order nonlocal function field equation is formulated.Based on the higher-order nonlocal function field equation, one-dimensional higher-ordernonlocal equation of non-Fourier heat conduction is developed. The higher-order nonlocalmodel and the classical homogenization model are compared with the fine finite elementsolution. The effects of differenet parameters and conditions are discussed. The results showthat the higher-order nonlocal model of non-Fourier heat conduction can be used to simulatethe dispersion and attenuation phenomena of heat wave propagation in periodic multiphasematerials under extreme heat impulse, and which shows the influence of the internal lengthscale parameter. However, the classical homogenization model is valid only when theexciation wavelength is larger than the characteristic length, while it is invalid when theexciation wavelength is smaller than or near the characteristic length. So the classicalhomogenization model can not simulate these phenomena.According to the higher-order nonlocal function field equation, one-dimensionalhigher-order nonlocal thermo-dynamic equation is developed. A one-dimensional slender barwith a periodic microstructure under heat impulse and dynamic impact load is studied. Thenumerical results show the solutions obtained by the proposed higher-order nonlocal model ofthermo-dynamics are generally in reasonable agreement with the fine finite element solutionand can be available for little computational cost to simulate the high frequency dynamicresponse and dispersion phenomena of dynamic wave propagation. It is demonstrated that thethe nonlocal model proposed is effective and valid.Mutli-dimensional problem of non-Fourier heat conduction is studied by a spatial andtemporal mutiscale high-order asymptotic homogenization method. The two-dimensionalnumerical examples are computed to analyse non-Fourier heat conduction in the differentmicrostructure of multiphase materials. The results further demonstrate thatmutli-dimensional higher-order nonlocal model obtained higher-order mathematicalhomogenization theory is valid and effective. However, in this work the higher-order nonlocalmodel is not simply extended from one-dimensional case to mutli-dimensional case. The maindifference is that the homogenized coefficients are obtained by the analytical approach inone-dimensional problem, while as for two-dimensional problem these coefficients are solvedby the numerical method.