The study of thermal stresses in a single long elastic fiber embedded in an infinite matrix

This work considered the micro-mechanical behavior of a long fiber embedded in an infinite matrix. Using the theory of elasticity, the idea of boundary layer and some simplifying assumptions, an approximate analytical solution was obtained for the normal and shear stresses along the fiber. The analytical solution to the problem was found for the case when the length of the embedded fiber is much greater than its radius, and the Young's modulus of the matrix was much less than that of the fiber. The analytical solution was then compared with a numerical solution based on Finite Element Analysis (FEA) using ANSYS. The numerical results showed the same qualitative behavior of the analytical solution, serving as a validation tool against lack of experimental results. In general this work provides a simple method to determine the thermal stresses along the fiber embedded in a matrix, which is the foundation for a better understanding of the interaction between the fiber and matrix in the case of the classical problem of thermal-stresses.

Meshfree Method for Prediction of Thermal Properties of Porous Ceramic Materials

In the presented thesis work, meshfree method with distance fields is applied to create a novel computational approach which enables inclusion of the realistic geometric models of the microstructure and liberates Finite Element Analysis(FEA) from thedependance on and limitations of meshing of fine microstructural feature such as splats and porosity.Manufacturing processes of ceramics produce materials with complex porosity microstructure.Geometry of pores, their size and location substantially affect macro scale physical properties of the material. Complex structure and geometry of the pores severely limit application of modern Finite Element Analysis methods because they require construction of spatial grids (meshes) that conform to the geometric shape of the structure. As a result, there are virtually no effective tools available for predicting overall mechanical and thermal properties of porous materials based on their microstructure. This thesis is a separate handling and controls of geometric and physical computational models that are seamlessly combined at solution run time. Using the proposedapproach we will determine the effective thermal conductivity tensor of real porous ceramic materials featuring both isotropic and anisotropic thermal properties. This work involved development and implementation of numerical algorithms, data structure, and software.