Thermoelastic Homogenization Analysis Of Uncertain Heterogeneous Materials Under Finite Deformation

Generally speaking,a heterogeneous material is a composite of two or more materials,or a combination of the same material in different states.Compared with the simple materials,the heterogeneous materials not only retain most of the excellent properties of the raw materials but also increase the properties which the raw materials do not have.Heterogeneous materials have been widely used in aerospace,transportation,bridges,construction and other aspects.Therefore,the development of a general approach to heterogeneous materials is one of the subjects of research on mechanics and materials.Homogenization method is an effective method for calculating macroscopic effective mechanical properties of heterogeneous materials.This method relies on the representative volume element(RVE)on the meso-scale,the effective properties of the material on the whole RVE can be obtained based on multi-scale finite element method.In this work,the stochastic and interval thermoelastic homogenization of a two-phase heterogeneous material is studied when considering the uncertainty existing in the microstructure of heterogeneous materials under the finite deformation framework.The main work of this dissertation is as follows.Firstly,the classification and application of heterogeneous materials,the relevant research background and present situation are introduced.Based on the theory of continuum mechanics,the definition,generation method and size convergence criterion of RVE are introduced.Aiming at the problem of thermo-elastic homogenization of heterogeneous materials under finite deformation,a multi-scale homogenization framework is constructed based on the hypothesis of scale separation and multiphysics theory,and thermo-elastic response of heterogeneous materials on the macroscopic scale is obtained.Then,on the basis of deterministic thermo-elasticity homogenization theory,the stochastic thermoelastic homogenization analysis model is constructed in the context of multi-scale finite element method and Monte Carlo method when considering the randomness of microstructural morphology of heterogeneous materials and the randomness of material parameters.After generating enough random simulation samples based on Monte Carlo method,the RVE is meshes and boundary conditions are applied on RVE,and the macroscopic stochastic effective properties and statistical eigenvalues of heterogeneous materials such as the first Piola-Kirchhoff stress tensor,heat flow tensor and sensitivities aswell as their means and mean variances are obtained by using multiscale homogenization method.Furthermore,considering the interval uncertainty of microstructural parameters of heterogeneous materials,the interval thermoelastic homogenization is studied based on multi-scale homogenization and optimization algorithm.Based on particle swarm optimization and genetic algorithm,the interval thermo-elastic homogenization model of two optimization algorithms is respectively constructed,and the interval value range of the macroscopic effective properties of heterogeneous materials is obtained by two optimization algorithms as well.Finally,in the random homogenization example,the effects of randomness of the parameters of the material constituents and the correlation between these random parameters on the randomness of the macroscopic effective quantity are investigated.In the interval optimization example,the uncertainty of interval parameter is considered fully,and the macroscopic effective property is solved by the improved PSO algorithm and genetic algorithm respectively,and the upper and lower bounds of the range of effective properties are obtained.The influence of interval variation of various parameters of heterogeneous materials on interval homogenization results is also investigated,and some meaningful conclusions are obtained.