It has been proven by J.C.Criscione that constitutive relations(mixed approach) based
on a set of five strain invariants (Beta-1, Beta-2, Beta-3, Beta-4, Beta-5) are useful and stable for experimentally
determining response terms for transversely isotropic material. On the other
hand, Rivlin’s classical model is an unsuitable choice for determining response terms
due to the co-alignment of the five invariants (I1, I2, I3, I4, I5). Despite this, however,
a mixed (Lagrangian and Eulerian) approach causes unnecessary computational time
and requires intricate calculation in the constitutive relation. Through changing the
way to approach the derivation of a constitutive relation, we have verified that using
an Eulerian approach causes shorter computational time and simpler calculation than
using a mixed approach does. We applied this approach to a boundary value problem
under specific deformation, i.e. finite extension and torsion to a fiber reinforced circular
cylinder. The results under this deformation show that the computational time
by Eulerian is less than half of the time by mixed. The main reason for the difference
is that we have to determine two unit vectors on the cross fiber direction from the
right Cauchy Green deformation tensor at every radius of the cylinder when we use a
mixed approach. On the contrary, we directly use the left Cauchy Green deformation
tensor in the constitutive relation by the Eulerian approach without defining the two
cross fiber vectors. Moreover, the computational time by the Eulerian approach is not influenced by the degree of deformation even in the case of computational time
by the Eulerian approach, possibly becoming the same as the computational time by
the mixed approach. This is from the theoretical thought that the mixed approach
is almost the same as the Eulerian approach under small deformation. This new
constitutive relation by Eulerian approach will have more advantages with regard
to saving computational time as the deformation gets more complicated. Therefore,
since the Eulerain approach effectively shortens computational time, this may enhance
the computational tools required to approach the problems with greater degrees of
anisotropy and viscoelasticity.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1667 |
| Date | 15 May 2009 |
| Creators | Song, Min Jae |
| Contributors | Rajagopal, Kumbakonam R. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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