Generalized Finite
Element Method for Modeling Nearly Incompressible
Bimaterial Hyperelastic Solids
K.R. Srinivasan1, K. Matous1,2
and P.H. Geubelle1
1Department of Aerospace Engineering
2Computational Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.
Abstract
An extension of the generalized finite element method to
the class of mixed finite element methods is presented to
tackle heterogeneous systems with nearly-incompressible
nonlinear hyperelastic material behavior. In particular,
heterogeneous systems with large modulus mismatch across
the material interface undergoing large strains are
investigated using two formulations, one based on a
continuous deformation map, the other on a discontinuous
one. A bimaterial patch test is formulated to assess the
ability of the two formulations to reproduce constant
stress fields, while a mesh convergence study is used to
examine the consistency of the formulations. Finally,
compression of a model heterogeneous propellant pack is
simulated to demonstrate the robustness of the
discontinous deformation map formulation.
Conclusions
The present work provides a numerical framework that
combines the generalized finite element method with the
classical mixed finite element method. Two formulations,
based on a continuous and discontinuous deformation map,
were derived and discretized for the motion of a
bimaterial nearly-incompressible hyperelastic solid. The
two formulations were assessed numerically on the
low-order Q
1/P
0 element, which is
very popular in engineering practice, using a bimaterial
patch test and mesh convergence studies were carried out
to evaluate the consistencies of the formulations. It was
observed that both the continuous and discontinuous
deformation maps yield convergent schemes for moderate
modulus mismatches, while the continuous deformation map
appears to be non-convergent for large mismatches.
Finally, an idealized heterogeneous solid propellant pack
is chosen as an example to demonstrate the capability and
robustness of the discontinuous deformation map
formulation.
Acknowledgment
This work was supported by the Center for Simulation of
Advanced Rockets (CSAR) under contract number B341494 by
the U.S. Department of Energy. K. Matous also
acknowledges support from ATK/Thiokol, ATK-21316 (Program
Managers, J. Thompson and Dr. I. L. Davis). The authors
would also like to thank Prof. C. A. Duarte for helpful
discussions and comments.
Download paper here
© 2009 Notre Dame and Dr.
Karel Matous