Stress Analysis Of An Ellipsoidal Inclusion
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The focus of the present thesis is to develop a mathematical model to calculate the stresses inside an ellipsoidal inclusion present in an infinitely extended matrix region and to validate the mathematically derived model by the Finite Element Method. To this end, a theoretical model has been developed to predict the stress inside an ellipsoidal inclusion. This model is based on equivalent inclusion method used to evaluate the stress distribution theoretically. Though there have been many theories to predict the stress distribution inside an ellipsoidal inclusion, its numerical validation is new despite its importance. A finite element model of a matrix-inclusion pair has been employed based on continuum mechanics approach. The interface surface between the matrix and the inclusion is modeled using suitable a contact element. The finite element analysis was carried out by assigning different properties for the matrix and inclusion region. Analysis with varying aspect ratio and elastic moduli of the inclusion region was also carried out to study the influence of the size and material property on the stress inside the inclusion. The finite element method shows that the stress distribution inside the inclusion is almost constant as predicted by the theoretical model. The above analysis also validates the use of the finite element method based on the continuum mechanics approach in studying the overall behavior of the inclusion problems.