Random Homogenization Analysis Of Heterogeneous Materials On Macroscopic Mechanical Properties

From the meso-mechanical theory of heterogeneous materials one obtains various nalytical and boundary estimates for the macroscopic effective properties, most of which are typically coarse. A popular method of acquiring the properties is to at first calculate the three physical fields of displacement, stress, and energy by the FEM (inite Element Method), thus deriving the required quantities by the homogenization procedure.In the case of elastic materials with infinitesimal deformations, this thesis establishes some numerical models for a random microstructure and its discrete meshes with MATLAB. Then the FEM will be used to compute the effective bulk and shear moludi of the microstructure after subjecting it to certain boundary conditions. The main work of this thesis consists of four sections.(a) A microstructure with random distributed particles has been constructed and analyzed under deterministic parameters of constituents.(b) The randomness of constituents" parameters of heterogeneous materials has been considered before the homogenization analysis is applied.(c) We’ve improved the RSA (Random Sequential Addition) algorithm for the generation of microstructure to meet the requirements of large volume fractions of particles, which proved to be solid and reliable.(d) Based on the improved RSA algorithm, the correlation of constituents’ parameters of heterogeneous materials is introduced to simulate the dependency of macroscopic effective bulk and shear moduli.The four steps above are progressively conducted, working as complements for traditional analysis of homogenization, and as stepping stones for the mechanical and multi-field coupling problems of elastic and inelastic materials with finite deformations.