Stochastic Homogenization Analysis Of Heterogeneous Materials Under Finite Deformation On Mechanics And Thermoelasticity

A two-phase heterogeneous material includes the matrix and the reinforcement(or inclusion). Heterogeneous materials have the advantages of the constituents, and at the same time the disadvantages of single material are abandoned. Additionally, heterogeneous materials are widely employed into every aspect of modern industries and life because of their outstanding qualities such as high intensity, low density, good workability and corrosion resistance, etc. Consequently, the investigations of their structural and mechanical properties have become more and more important. During the process of their machining and manufacture, materials are inevitably influenced by many uncertain factors. So it is essential to take into account the randomness of and correlation among the microscale properties when seeking the effective properties of heterogeneous materials.In this work, stochastic homogenization analysis of heterogeneous materials is addressed in the context of elasticity and thermoelasticity under finite deformations. Firstly, the classification, application, the background and the latest research of heterogeneous materials are introduced. Then the definition and generation of the RVE are given explicitly. On the basis of knowledge about RVE, both homogenization methods in the context of elasticity and thermoelasticity are introduced based on finite element method, in which the elaboration of boundary conditions and the approach to the effective properties under both micro-scale and macro-scale are displayed. On the basis of Monte Carlo method, the random homogenization frameworks under both mechanics and thermoelasticity are presented to get the overall micro-scale properties of heterogeneous material and their numerical characteristics. At the end, examples of random homogenization are given, where the randomness of the microstructural morphology and of the material properties of the constituents as well as the correlation among these random quantities are fully considered. A three-dimensional representative volume element of the two-phase heterogeneous material with randomly distributed particles is firstly generated by random sequential addition. The size of the RVE is then identified with a numerical convergence scheme. With enough samples employed, the random effective properties of the heterogeneous material are tackles by joint methods of multiscale, finite element and Monte Carlo. In the mechanical analysis under finite deformations, different boundary conditions are applied to the RVE to get effective properties such as tangent tensor, first Piola-Kirchhoff stress, strain energy, etc. For thermoelasticity, the random homogenization analysis is divided into two phases, i.e. purely mechanical and purely thermal, to get random effective properties such as stress tensor, heat flux tensor, deformation gradient, etc. The numerical characteristics of the effective properties are tackled and the influence of different random cases on the random effective quantities is finally analyzed.