Bifurcation and stability of spherical shells and cavities in a plastic medium [electronic resource].

Jefferson, George Joseph, Jr.
175 p.
Contained In:
Dissertation Abstracts International 60-04B.

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Mechanical engineering.
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Penn dissertations -- Mechanical engineering and applied mechanics. (search)
Mechanical engineering and applied mechanics -- Penn dissertations. (search)
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Mode of access: World Wide Web.
The bifurcation and stability of a spherical void embedded in an incompressible matrix material and subjected to hydrostatic loading has relevance to the collapse of thick walled pressure vessels as well as to the densification of porous materials by plastic deformation. Porous materials are commonly modeled using an isolated spherical void calculation. Here, we consider the possibility of bifurcation under hydrostatic load as a possible mechanism for void shape change. Bifurcation and subsequent non spherical deformation of a sphere is examined by direct application of Hill's variational uniqueness criteria as well as with a finite element model. In plastic buckling problems, calculations using path independent deformation theory model can show a loss of uniqueness that a J2 flow theory model fails to predict. However, the restriction of the deformation model to nearly proportional stressing makes it inadequate for post bifurcation analysis. A comer theory has been implemented to capture the bifurcation, yet provide a physically realistic description of the non proportional post bifurcation behavior. We have used the deformation and comer models to predict the critical load and associated change in void shape. For small volume fractions our results are in agreement with the results of Bassani, Durban, and Hutchinson (1979) for an isolated void. The evolution of void shape changes beyond the bifurcation point is investigated using an axisymmetric finite element model. For the post bifurcation calculation it proved necessary to use a flow theory material and to seed the calculation with an imperfect initial cavity shape. The shape of arbitrarily small imperfections are retained as the cavity collapses, with ellipsoidal imperfections leading to needle or penny shaped crack-like voids and higher order imperfections resulting in more complicated surface buckling modes.
Thesis (Ph.D. in Mechanical Engineering and Applied Mechanics) -- University of Pennsylvania, 1999.
Source: Dissertation Abstracts International, Volume: 60-04, Section: B, page: 1814.
Supervisor: John L. Bassani.
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School code: 0175.
Bassani, John L., advisor
University of Pennsylvania.
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