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

Document Type



Master of Science (MS)


Mechanical Engineering

First Advisor's Name

Cesar Levy

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Kuang-Hsi Wu

Third Advisor's Name

Norman D. H. Munroe

Fourth Advisor's Name

Ivan E. Esparragoza

Date of Defense



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.




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