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https://hdl.handle.net/2142/71678
Description
Title
On Residual Stress in an Elastic Body
Author(s)
Hoger, Anne Georgacas
Issue Date
1984
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Abstract
Residual stress is defined as the stress field supported by a body in the absence of external forces. Thus, the residual stress is in equilibrium with zero body force, is symmetric, and gives rise to zero surface traction.
An elastic body with a particular material symmetry can admit only those residual stress fields that commute with the elements of the symmetry group of the material. Using this condition, one can obtain the forms for residual stress fields appropriate to specific material symmetries. Here the additional restrictions imposed by equilibrium and the zero traction condition are explored. It is shown that if a body is isotropic it supports no residual stress. For bodies that are transversely isotropic, among other results, it is established that the residual stress must vanish if the axis of symmetry is uniform. Bodies composed of material with rhombic or monoclinic symmetry are also considered. Additional results can be found in the context of particular body geometries. As an example, states of residual stress possible in a transversely isotropic right circular cylinder are discussed.
The rest of the thesis is devoted to the construction of a theoretical framework with which to explore the possibility of the nondestructive mechanical determination of residual stress. The body is supposed to support an unknown residual stress field in its reference configuration, and it is assumed that the body responds in a linearly elastic manner to small deformations from the reference configuration. The residual stress appears explicitly in the corresponding constitutive equation, and we treat it as constitutive information which we want to determine.
The constitutive equation valid for a linearly elastic body which supports a residual stress is derived and discussed, and the basic equations of the theory are displayed. These equations are then used to construct boundary value problems that allow particular forms of residual stress to be written explicitly in terms of traction boundary data. The uniqueness of the resulting expression for the residual stress is discussed.
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