Description
- Abstract:
- Compatibility conditions for various strain measures are well known in both small and finite strain kinematics. For many plane deformation problems in solid mechanics, such conditions enable boundary value problems to be formulated using strains, stresses, or a generating potential function, as the fundamental dependent variable(s). This thesis is concerned with the compatibility issue for the rotation field, as it relates to the study of plane deformations. Although it is not a direct measure of the distortion in a deformation, the rotation associated with a deformation and its variation from point to point within a continuous body turns out to carry quite a bit of information about the actual deformation. Presented here, is a methodology showing that any planar proper orthogonal tensor can serve as a rotation field and can be used to construct a plane finite deformation. Various applications of the method are analyzed accompanied by examples, in which specific deformations examined are: local deformations around a point or curve of interest, twinning and two-phase deformations, and finally area preserving deformations.
- Notes:
- Thesis (Ph.D. -- Brown University (2013)
Access Conditions
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Citation
Rizza, Gregory James,
"Plane Deformations Generated by Prescribed Finite Rotation Fields: Issues and Applications"
(2013).
Mechanics of Solids Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0TD9VPC
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Mechanics of Solids Theses and Dissertations
Theses and Dissertations for the Mechanics of Solids department....