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CivilComp Proceedings
ISSN 17593433 CCP: 88
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis
Paper 258
On the Correlation of Theory and Experiment for Transversely Isotropic Nonlinear Incompressible Solids M.H.B.M. Shariff^{1}, B.A. Mahad^{2} and A.A. Zainal^{2}
^{1} Kalifa University of Science, Technology and Research, United Arab Emirates
M.H.B.M. Shariff, B.A. Mahad, A.A. Zainal, "On the Correlation of Theory and Experiment for Transversely Isotropic Nonlinear Incompressible Solids", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 258, 2008. doi:10.4203/ccp.88.258
Keywords: transverselyisotropic, nonlinear, constitutiveequation, principalaxes.
Summary
A novel strain energy function for
finite strain deformations of transversely isotropic elastic solids which is a function
five invariants that have immediate physical interpretation has recently been developed. Three of the five
invariants are the principal stretch ratios and the other two are squares of the dot product between
the preferred direction and two principal directions of the right stretch tensor. A strain energy function,
expressed in terms of these invariants, has a symmetrical property almost similar to that of an isotropic
elastic solid written in terms of principal stretches. This constitutive equation is attractive if principal
axes techniques are used in solving boundary value problems and experimental advantage is demonstrated
by showing a simple triaxial test can vary a single invariant while keeping the remaining invariants fixed.
Explicit expressions for the weighted Cauchy response functions are easily obtained since the response function
basis is almost mutually orthogonal. In this paper a specific form of the strain energy function for incompressible materials
which is linear with respect to its physical parameters is developed. When a curve fitting method
is (sensibly) applied on an experimental data, the values of the parameters are obtained
uniquely via a linear positive definite system of equations. The theory compares well with experimental data and
the performance of the proposed specific form is discussed. A constitutive inequality, which may reasonably be imposed upon the material
parameters, is discussed.
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