M.Sc Thesis

M.Sc StudentHollander Yaniv
SubjectBifurcation Phenomena around a Spherical Inclusion
DepartmentDepartment of Aerospace Engineering
Supervisor PROFESSOR EMERITUS David Durban


This thesis summarizes research work on the subject of bifurcation and loss of mechanical stability phenomena around a spherical inclusion. In the problem studied a spherical inclusion of one material is growing against an outer matrix made of a different material. During the initial growth process the inclusion expands in a spherical symmetric pattern, where continuity between the inclusion and its surroundings is preserved. At a critical stage bifurcation can occur, implying that the primary spherical symmetric shape of the inclusion becomes a-morphed. As a result, separation between the inclusion and the surrounding can happen along with fragmentation of the different phases.

There are many examples of instability induced by inclusion growth, taken from fields of engineering, physics and biology. One example is solid rocket fuel made of a polymeric matrix containing small metallic particles that expand against the matrix during the burning process of the fuel causing loss of mechanical stability. Another example, taken from the field of biology, is concerned with a small spherical tumor that grows against a healthy tissue that surrounds it. The growth of the tumor can induce rapture of the tissue, and can also act as a mechanical stimulator for transformation of the tumor from benign to malignant.

In this research a variety of materials, including hyperelastic compressible isotropic solids, were studied. However, since most of the derivations in the thesis are general, without necessarily focusing on specific material, it is possible to expand the applicability of the analysis for more general materials and liquids.

One of the main finding exposed in the research is that bifurcation in this type of growth process is possible. The characteristics of the bifurcated fields are highly sensitive to constitutive response and to the strength differential between the inclusion and the matrix.