On the stress in an internally constrained elastic material
Marlow, Randall Scot
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https://hdl.handle.net/2142/20893
Description
Title
On the stress in an internally constrained elastic material
Author(s)
Marlow, Randall Scot
Issue Date
1989
Committee Member(s)
Carlson, Donald E.
Department of Study
Mechanical Science and Engineering
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Mathematics
Language
eng
Abstract
The admissible deformation gradients at an internally constrained elastic material point form a closed submanifold in the space of invertible tensors. This submanifold, the constraint manifold, is described locally in terms of a manifold structure on the invertible tensors. Constraint functions arise naturally from the submanifold properties of the constraint manifold.
The stress in the constrained material is determined by the deformation gradient only to within an additive reaction stress. A representation for the reaction stress involving the gradients of the constraint functions is derived. The determinate stress is assumed to be given by a function defined on the constraint manifold and having normalized values.
Symmetry of internally constrained elastic materials is investigated, as well as the principle of material indifference. These basic concepts are discussed in relation to the stress spaces.
"A theory of constrained elastic materials for ""small"" displacement gradients is derived directly from the general theory. Since an explicit relation for the reaction stress exists, the derivation is straight-forward. The results are significantly different from what has been done previously. To illustrate the differences, the torsion of an inextensible cylinder is discussed."
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