In finite elasticity, while developing representation for stress, it is customary to require
the reference configuration to be stress free. This study relaxes this requirement
and develops representations for stress from a stressed reference configuration. Using
the fact that the value of Cauchy stress in the current configuration is independent of
the choice of the reference configuration, even though the formula used to compute
it depends on the choice of the reference configuration, the sought representation is
obtained. It is then assumed that there exists a piecewise smooth mapping between
a configuration with prestresses and a configuration that is stress free, and the representation
obtained above is used to study the mechanical response of prestressed
bodies. The prestress fields are obtained by directly integrating the balance of linear
momentum along with the traction free boundary condition. Then, different classes
of boundary value problems for the type of inhomogeneous and prestressed bodies of
interest are formulated and studied. For the cases studied, it is found that even the
global measures like axial-load required to engender a given stretch ratio for a prestressed
body vary from the homogeneous stress free bodies, though not significantly.
The local measures - stress and deformation - in a prestressed body differ considerably
from their homogeneous stress free counterparts. The above gained knowledge is applied
to understand the mechanics of circumflex arteries obtained from normotensive and hypertensive micro-mini pigs. It is found that the deformation of these arteries
when subjected to inflation and axial extension is not of the form r = r(R), õ =
ã, z = Z. Comparison is also made between the response of an artery at various
levels of smooth muscle activation and stretch ratio as well as normotensive and
hypertensive specimens, using statistical methods.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4241 |
| Date | 30 October 2006 |
| Creators | Umakanthan, Saravanan |
| Contributors | Humphrey, Jay, D., Rajagopal, Kumbakonam |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 4859048 bytes, electronic, application/pdf, born digital |
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